Thanks for the comments, I’ll respond more later. For now, on this point, I would say that I’m not sure your point does stand. You said: “Jesus as a man does not necessarily mean Jesus as God is also a man because there is a non mingling.”
Now as you say, God knows best. But as I understand it Jesus-as-God and Jesus-as-man are categories that could be useful for describing particular attributes of Jesus, some of which are in keeping with the divine nature, some with his human nature. When it comes to the question of who Jesus is, however, we simply say: Jesus is God and Jesus is man and there is only one Jesus, one person. Mary is the mother of the man Jesus, but we also call her the mother of God, because Jesus is God. Therefore she is the mother of a man who is God; therefore God is a man.
Now we believe that this person, Jesus, the son of God, the Word of God, created both human sexes in his image, but he eternally foresaw and predestined his plan of redemption, his plan for uniting humans to himself by letting them share in his knowledge and love, and that eternal plan - as Catholics understand it - obviously includes the part about him becoming human, and becoming human as a male, not a female - as well as everything else, such as honoring his mother by making her to be the preeminent figure of redeemed humanity, complementary to himself as the preeminent figure of (as well as the fullness of being of) God HIMself. Neither man nor woman is neglected or denigrated in God’s plan, but they are differentiated, and certainly God knows best why it eternally is, was, and ever shall be more appropriate for God’s nature to be/to have been joined to human nature as a male, rather than as a female.