Why was Zechariah Made Mute?

A reader writes:

I’ve recently read the Bible passage in Luke where it’s stated that Zechariah was made mute because he did not believe in the angel Gabriel’s propehcy on the conception of his future son, John the Baptist.

Contrasting this with the annunciation of Mary, who also questioned the angel, but was not made mute as well. From what I understand, it is because Zechariah doubted but Mary never once did. However, I cannot find it explicitly stated so in the Bible.
Can you explain why Zechariah was made mute? My friend thinks this shows that God does not like being questioned and I would like to know how to answer him.

Actually it is explicitly stated by Gabriel: ”
“I am Gabriel, who stand in the presence of God; and I was sent to speak to you, and to bring you this good news. And behold, you will be silent and unable to speak until the day that these things come to pass, because you did not believe my words, which will be fulfilled in their time.” (Luke 1:19-20)

Meanwhile, Mary asks questions, but does not doubt. That’s why she is able to say, “Behold, I am the handmaid of the Lord; let it be to me according to your word.” (Luke 1:38). Luke’s whole point is to contrast the disbelieving questions of Zechariah and the believing questions of Mary. The latter are asked in order to find things out; the former are asked in order to keep from finding things out.

It is simply not so that the God revealed in Scripture “does not like being questioned”. Scripture is, in fact, stuffed with questions directed to God and answered by God. What God disciplines Zechariah for is not asking questions, but not expecting Him to answer. The answer Zechariah gets is perfectly suited to his spiritual condition and is, like all things God does, done in charity and with an eye on revealing Himself to Zechariah. And, by the way, it works. Zechariah’s question is answer and Zechariah believes.