His words will be in blue. Translations from the Portugese of his book will be made with Google Translate (with an occasional additional modification). I will use RSV for Bible translations.
The existence of purgatory is based on theological assumptions and specific beliefs rather than concrete evidence. There is no objective proof or scientific knowledge of its existence, and the idea was developed and sustained mainly by specific religious doctrines and traditions. Without any factual basis, it becomes difficult to justify the existence of an intermediate place where souls are purified. (p. 27)
Clearly, this teaching lacks a biblical basis, . . . (p. 30)
In fact, the central, essential ideas concerning purgatory are massively present in Scripture. The “nutshell” argument for purgatory is that we must be without sin to enter into God’s presence (Eph 5:5; Heb 12:14 [“holiness without which no one will see the Lord”]; 2 Pet 3:13 [“. . . in which righteousness dwells”]; Rev 21:8, 27 [“nothing unclean shall enter it”]; 22:3, 14-15 [“Blessed are those who wash their robes, . . . that they may enter the city by the gates”). Therefore, God must purge or wash away our sin to make us fit to be in heaven with Him. All agree so far. The only disagreement is whether this “divine cleansing” takes place in an instant or is more of a process. It’s merely a quantitative difference; not an essential one. Purgatory is indicated most directly in 1 Corinthians 3:13, 15:
Each man’s work will become manifest; for the Day will disclose it, because it will be revealed with fire, and the fire will test what sort of work each one has done. . . .  If any man’s work is burned up, he will suffer loss, though he himself will be saved, but only as through fire.
Protestant commentators fully agree that sin must be purged prior to anyone entering heaven (and this is the central idea and purpose or nature of purgatory). Here’s what several of them observe about Revelation 21:27:
Ellicott’s Commentary for English Readers The gates stand open always, but no evil thing may find a home there. The emphatic repetition here (see Revelation 21:8) of the idea that all sin is excluded, is in harmony with all other Scripture: no unholiness can dwell in the presence of God.
Matthew Henry’s Concise Commentary Nothing sinful or unclean, idolatrous, or false and deceitful, can enter. All the inhabitants are made perfect in holiness. Now the saints feel a sad mixture of corruption, which hinders them in the service of God, and interrupts their communion with him; but, at their entrance into the holy of holies, they are washed in the laver of Christ’s blood, and presented to the Father without spot. None are admitted into heaven who work abominations. It is free from hypocrites, such as make lies. As nothing unclean can enter heaven, let us be stirred up by these glimpses of heavenly things, to use all diligence, and to perfect holiness in the fear of God.
Barnes’ Notes on the Bible [N]othing will be found in that blessed abode which is unholy or sinful. It will be a pure world, . . .
Matthew Poole’s Commentary [T]his strongly denying particle is brought to make the bar excluding all unclean persons from heaven evident.
The Bible also often refers to this same purging process taking place before we die: the very common biblical theme of God’s chastising or purifying His people. By analogy, this shows us the same notions that lie behind the apostolic and Catholic doctrine of purgatory (methods of how God works, so to speak). When these passages are included, one can rather easily find (as I did) as many as fifty biblical passages that are relevant to purgatory.
Scripture refers to a purging fire (in addition to 1 Corinthians 3 above): whatever “shall pass through the fire” will be made “clean” (Num 31:23); “Out of heaven he let you hear his voice, that he might discipline you; and on earth he let you see his great fire, and you heard his words out of the midst of the fire” (Dt 4:36); “we went through fire” (Ps 66:12); “our God is a consuming fire” (Heb 12:29); “do not be surprised at the fiery ordeal which comes upon you to prove you” (1 Pet 4:12); We also see passages about the “baptism of fire” (Mt 3:11; Mk 10:38-39; Lk 3:16; 12:50).
The Bible makes frequent use also of the metaphor of various metals being refined (in a fire): “when he has tried me, I shall come forth as gold” (Job 23:10); “thou, O God, hast tested us; thou hast tried us as silver is tried” (Ps 66:10); “The crucible is for silver, and the furnace is for gold, and the LORD tries hearts” (Prov 17:3); “I will turn my hand against you and will smelt away your dross as with lye and remove all your alloy” (Is 1:25); “I have refined you, . . . I have tried you in the furnace of affliction” (Is 48:10); “I will refine them and test them” (Jer 9:7); “I will put this third into the fire, and refine them as one refines silver, and test them as gold is tested” (Zech 13:9); “he is like a refiner’s fire, and like fullers’ soap; he will sit as a refiner and purifier of silver, and he will purify the sons of Levi, and refine them like gold and silver” (Mal 3:2-3); “. . . your faith, more precious than gold which though perishable is tested by fire” (1 Pet 1:6-7).
God cleansing or washing us is another common biblical theme: “Wash me thoroughly from my iniquity, and cleanse me from my sin! . . . Purge me with hyssop, and I shall be clean” (Ps 51:2, 7); “Blows that wound cleanse away evil; strokes make clean the innermost parts” (Prov 20:30; cf. 30:12); “the Lord shall have washed away the filth of the daughters of Zion and cleansed the bloodstains of Jerusalem from its midst by a spirit of judgment and by a spirit of burning” (Is 4:4); “I will cleanse them from all the guilt of their sin against me” (Jer 33:8); “I will sprinkle clean water upon you, and you shall be clean from all your uncleannesses” (Ezek 36:25); “cleanse them from sin and uncleanness” (Zech 13:1); “our hearts sprinkled clean from an evil conscience and our bodies washed with pure water” (Heb 10:22); “he was cleansed from his old sins” (2 Pet 1:9); “the blood of Jesus his Son cleanses us from all sin” (1 John 1:7).
Divine “chastisement” is taught clearly in many passages: “as a man disciplines his son, the LORD your God disciplines you” (Dt 8:5); “do not despise the LORD’s discipline or be weary of his reproof,” (Prov 3:11); “I will chasten you in just measure” (Jer 30:11); “God who tests our hearts” (1 Thess 2:4); “For the Lord disciplines him whom he loves, and chastises every son whom he receives. It is for discipline that you have to endure. God is treating you as sons; for what son is there whom his father does not discipline? . . . he disciplines us for our good, that we may share his holiness” (Heb 12:6-7, 10).
We are subject to God’s indignation or wrath, insofar as we sin: “God will bring every deed into judgment” (Ecc 12:14); “I will bear the indignation of the Lord because I have sinned against him, . . . He will bring me forth to the light” (Mic 7:9).
Purgatory is “written all over” the passages above. Once upon a time I didn’t make the connection of what seems so obvious to me now. I think there are many who (like myself) may be able to be persuaded to see that the Bible is far more “Catholic” than they had ever imagined.
Many religions teach that salvation is achieved through faith and God’s grace, not through human actions. But purgatory suggests that souls must be purified through suffering and penance to achieve complete salvation. (p. 27)
God is doing most of the “actions” in purgatory, as can be seen in the above passages. It’s He Who is purifying, washing, chastising, refining, testing, cleansing, disciplining, purging, etc. Purgatory doesn’t “suggest” anything. It’s God Who revealed in His revelation that sins have to be purged and that no sinner, with sin in his soul can enter heaven. It’s not allowed there. Sin must be actually purged and cleansed, not just the superficial, surfacey, pretend, external, merely declarative justification that Protestantism dreamt-up, contrary to Holy Scripture and all previous tradition.
This perspective places an additional burden on individuals, shifting the focus away from mercy and divine love. Another criticism of purgatory is that it seems to contradict the idea of an almighty and compassionate God. If God is infinitely merciful, why would he allow the souls of the elect to undergo a process of additional suffering after death? (p. 27)
Purgatory is no more of a “burden” than has always been part of the Christian life:
Romans 12:1 . . . present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship.
1 Corinthians 3:17 . . . For God’s temple is holy, and that temple you are.
2 Corinthians 7:1 Since we have these promises, beloved, let us cleanse ourselves from every defilement of body and spirit, and make holiness perfect in the fear of God.
Ephesians 4:24 and put on the new nature, created after the likeness of God in true righteousness and holiness.
Colossians 3:12 Put on then, as God’s chosen ones, holy and beloved, compassion, kindness, lowliness, meekness, and patience,
1 Thessalonians 2:10 You are witnesses, and God also, how holy and righteous and blameless was our behavior to you believers;
Hebrews 12:14 Strive for peace with all men, and for the holiness without which no one will see the Lord.
1 Peter 1:15-16 but as he who called you is holy, be holy yourselves in all your conduct;  since it is written, “You shall be holy, for I am holy.”
2 Peter 3:11 Since all these things are thus to be dissolved, what sort of persons ought you to be in lives of holiness and godliness,
A loving and merciful God, of course, made all these commands, through His apostles. Repetition is a great teacher: “For the Lord disciplines him whom he loves, and chastises every son whom he receives. It is for discipline that you have to endure. God is treating you as sons; for what son is there whom his father does not discipline? . . . he disciplines us for our good, that we may share his holiness” (Heb 12:6-7, 10).
The most serious criticism is this: the idea of purgatory nullifies fully the sacrifice of Jesus on the cross. (p. 28)
If that’s the case, then the Bible is self-contradictory, since it refers to “holiness without which no one will see the Lord” (Heb 12:14) and states that “nothing unclean shall enter” heaven (Rev 21:27) and that “Blessed are those who wash their robes, . . . that they may enter the city by the gates” (Rev 22:14). Do all these inspired portions of the infallible revelation of Holy Scripture “nullify” Jesus’ sacrifice on the cross, too?
In Romans 8:1, Paul states, “Therefore now no condemnation there are for those who are in Christ Jesus, who do not walk according to the flesh, but according to the Spirit.” (p. 28)
Exactly. Whoever is truly “in” Jesus will be saved.
Now, if there is no condemnation or suffering for those who are in Christ, what is the reason for purgatory? (p. 28)
Quite obviously, to prepare a still sinful soul for entering a place where no sin is permitted. See the above relevant biblical passages.
The Bible is very clear. Whether you are in Christ or you are not, there is no middle ground. If you are not in Christ, what awaits you in the afterlife is hell. (p. 28)
Exactly. Everyone in purgatory is saved. This is a non-issue. The issue isn’t salvation, but rather, the necessity of purification prior to entering a totally holy place.
The doctrine of purgatory . . . suggests that souls must go through a process of purification and atonement before entering heaven. (p. 29)
The Bible teaches that souls must go through a process of purification and atonement before entering heaven, per all of my prooftexts above.
If salvation is a free and unconditional gift offered by God, why would it be necessary to go through a additional purification process? (p. 29)
Precisely because no sin is allowed in heaven, and we still have much sin in our lives and souls. In heaven there are no more games, such as imputed justification.” There, we will be — must be — actually holy, not merely declared so, in some sort of equivocating word game. Protestants themselves stress that we are not actually holy, only declared to be, even though we aren’t. Therefore, to enter a place that requires actual holiness (if we go by Protestants’ own premises), we have to somehow be transformed in actuality. And that is purgatory. And we can begin the process right now in this life, so the entrance will be much easier when the time comes.
Furthermore, the doctrine of purgatory can also lead to a “works” mentality as opposed to “faith.” People may feel that need to perform good works or penances to guarantee their entry into heaven, instead of trusting in the grace of God. (p. 29)
The two things are not mutually exclusive. Good works are an intrinsic part of faith, and are central in fifty biblical passages that discuss being saved and entrance into heaven. St. Paul alone writes at least fifty passages that tie together grace, faith, and works, in an organic, inseparable whole.
Catholic theologians developed the doctrine of the “two judgments,” a conception absent in the Eastern church. According to this Roman Catholic perspective, there are two judgments: the individual judgment, that occurs immediately after death, beginning the intermediate state of those who have passed away, and the general judgment, which takes place at the second coming of Jesus, at the end of the intermediate state. . . . individual judgment invented by Rome (p. 32)
It could hardly have been “invented” by us, since it is present in Scripture:
John 3:18, 36 He who believes in him is not condemned; he who does not believe is condemned already, because he has not believed in the name of the only Son of God. . . .  He who believes in the Son has eternal life; he who does not obey the Son shall not see life, but the wrath of God rests upon him.
Hebrews 9:27 . . . it is appointed for men to die once, and after that comes judgment,
Moreover, in Jesus’ story about Lazarus and the rich man (Luke 16), it’s clear that both men have been judged and that their fate is sealed, even though they are in Hades (divided into good and bad compartments). The rich man is condemned, and Lazarus is saved. This was all determined before the Final Day of Judgment; indeed, while Jesus still walked the earth.
Fourthly, Jesus referred to Judas as “the son of perdition” (Jn 17:2), meaning that he was damned for all eternity.
[M]ost problematic . . . for Catholic doctrine, the Bible nowhere mentions an individual judgment occurring in an intermediate state before the resurrection, . . . This doctrine simply has no biblical support, . . . (p. 33)
This isn’t true. The rich man in Hades has been condemned:
Luke 16:23-25 and in Hades, being in torment, he lifted up his eyes, and saw Abraham far off and Lazarus in his bosom.  And he called out, ‘Father Abraham, have mercy upon me, and send Lazarus to dip the end of his finger in water and cool my tongue; for I am in anguish in this flame.’  But Abraham said, `Son, remember that you in your lifetime received your good things, and Lazarus in like manner evil things; but now he is comforted here, and you are in anguish.
Fifthly, we know that certain people have been rejected by God. For example, we have King Saul, whom God turned away from (1 Sam 16:7, 14; 18:12; 19:9), and whom the prophet Samuel (appearing after death) confirmed as one who was forsaken by God (“the LORD has turned from you and become your enemy”: 1 Sam 28:16). How can such a person be saved? Saul died in the forsaken state, as an enemy of God! So we know where he went. He was already judged.
Sixthly, many bad Kings of Judah and Israel were described as having done “evil in the sight of the Lord.” Excepting a repentance on their part, if they were evil all the way to their deaths, we can reasonably assume that they were damned.
Summary: Juan Oliveira attempts many futile & bad arguments against purgatory, but fails to interact at all with scores of relevant passages that I bring up from Holy Scripture.