It's subtle like when Jesus said "Why do you call me good". You have to be paying attention to hear what He is saying. "Of men born of women". But we know Jesus is greater than John therefore... This is not to say that she was not a vessel, but He is not of her, not her egg.
Indeed we do, but Jesus won't be the one to tell you that. Didn't he tell his disciples not to do things like that?
I still say you're drawing your own conclusions with that verse.
Then why did God pick a woman? Why not just create Jesus as he did Adam?
So you would hold that the following is not a messianic passage?
And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel. (Genesis 3:15, KJV)