The Annunciation, Philippe de Champaigne, 1644 [public domain / Wikimedia Commons]
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Here we have another massive misunderstanding as to the patristic and Catholic meaning of a striking phrase: similar to the false perception of “Mother of God”.
Having a child conceived by the Holy Spirit has no direct analogy, because it was a one-time extraordinary event, in order to bring about the incarnation. We should fully expect to have some difficulty understanding it. But Christianity is filled with such anomalies, wonders, and paradoxes. How could Jesus be fully God and fully man? Run-of-the-mill logic cannot accept this, anymore than it can grasp the Trinity (hence many heretics deny both). It requires the eyes of faith and a comprehension of the “both/and” biblical, Hebraic outlook.
St. Augustine (354-430) stated that “Mary was that only one who merited to be called the Mother and Spouse of God.” (Sermon 208). Scripture speaks in terms of the bride being the Church, and makes analogies between marriage and Christ and His Church. So why should there be controversy about Mary being the spouse of the Holy Spirit?
By the same general reasoning that applies to Theotokos (arguing solely from the Bible, not Catholic tradition), it seems to me that “spouse of God” would also be appropriate and non-objectionable. That Jesus’ conception was of the Holy Spirit as a sort of “Father” is plain in the Bible:
Matthew 1:18-20 (RSV) Now the birth of Jesus Christ took place in this way. When his mother Mary had been betrothed to Joseph, before they came together she was found to be with child of the Holy Spirit;  and her husband Joseph, being a just man and unwilling to put her to shame, resolved to divorce her quietly.  But as he considered this, behold, an angel of the Lord appeared to him in a dream, saying, “Joseph, son of David, do not fear to take Mary your wife, for that which is conceived in her is of the Holy Spirit;” (cf. Lk 1:31, 34-35)
If we ask, then, “Who is Jesus’ father?” (in terms of the origin of His conception), it’s not Joseph, but the Holy Spirit in one sense, and God the Father in another. Multiple senses and meanings and applications are common in Holy Scripture.
By analogy, then, if Jesus’ parents were Mary and the Holy Spirit, then by simple analogy it follows that Mary (in this particular sense, and this alone) is the “spouse of God” just as she was the Mother of God.
Likewise, “spouse of God” is thought to imply an equality with God, when in fact it’s only a limited analogical description based on Mary’s relation to the Holy Spirit in the matter of the conception of Jesus. This description is no more “unbiblical” or non-harmonious with scriptural thought than St. Paul saying “we are God’s fellow workers” (1 Cor 3:9; cf. 2 Cor 6:1), or St. Peter referring to men becoming “partakers of the divine nature” (2 Pet 1:4; cf. 1 Jn 3:2). These are similarly understood as not entailing equality with God.
Along these lines, there are many biblical passages about Israel or the Church being the “bride” of God the Father or Jesus Christ, God the Son:
Isaiah 54:5 For your Maker is your husband, the LORD of hosts is his name; . . .
Isaiah 62:5 . . . as the bridegroom rejoices over the bride, so shall your God rejoice over you.
Jeremiah 31:32 . . . my covenant which they broke, though I was their husband, says the LORD. (cf. 3:20)
Hosea 2:16, 19-20 “And in that day, says the LORD, you will call me, `My husband,’ and no longer will you call me, `My Ba’al.’ . . .  And I will betroth you to me for ever; . . . (cf. 4:12; 9:1)
Matthew 9:15 And Jesus said to them, “Can the wedding guests mourn as long as the bridegroom is with them?” (cf. Mk 2:19-20; Lk 5:34-35; Mt 25:1-10)
2 Corinthians 11:2 I feel a divine jealousy for you, for I betrothed you to Christ to present you as a pure bride to her one husband.
Ephesians 5:28-29, 32 Even so husbands should love their wives as their own bodies. He who loves his wife loves himself.  For no man ever hates his own flesh, but nourishes and cherishes it, as Christ does the church, . . .  This mystery is a profound one, and I am saying that it refers to Christ and the church (cf. Rev 19:7; 21:2; 21:9)
Given all of this biblical data, saying that Mary is the “spouse of God” should not present any difficulty at all to anyone who accepts the Bible as God’s inspired revelation. The only possible objection would come from not understanding what is meant by the phrase in the first place.