"Why do Catholics refer to Mary as 'Queen'?" A Biblical Response

Quite simply, because that's how you refer to the mother of a king, and in this case, the Mother of the Kings of Kings.  When the angel Gabriel announced Jesus' birth to Mary he said, "the Lord God will give to him the throne of his father David" (Lk 1:32). Solomon had been the first successor to sit upon the throne of David, and look at the story God inspired the author of the Old Testament's 1 Kings to record regarding Solomon and his mother Bathsheba:

So Bathshe′ba went to King Solomon, to speak to him on behalf of Adoni′jah. And the king rose to meet her, and bowed down to her; then he sat on his throne, and had a seat brought for the king’s mother; and she sat on his right. Then she said, “I have one small request to make of you; do not refuse me.” And the king said to her, “Make your request …” (1 Kings 2:19-20)

The king's mother, seated upon a throne at the king's right hand - the place of authority.  The kings of Israel, you see, took many wives (a practice that got Solomon into trouble later on).  None of the wives received the title of queen; rather, it went to the king's mother.  So when Jesus came as the ultimate successor to David's throne, His Mother became the Queen Mother.  Now granted, just as Jesus is not a King patterned after the monarchs of this world, neither is His Mother's Queenship.  But if Jesus is a King, then His Mother is most assuredly a Queen.  And what is the scope of Jesus' Reign?  All of creation.

Here is a queenly-image of the Mother of the Messiah from the Book of Revelation:

And a great portent appeared in heaven, a woman clothed with the sun, with the moon under her feet, and on her head a crown of twelve stars; she was with child and she cried out in her pangs of birth, in anguish for delivery ... she brought forth a male child, one who is to rule all the nations with a rod of iron, but her child was caught up to God and to his throne ... (Rev 12:1-5)