Seriously, people? Of course Jesus was “born of woman.” Paul makes a big point of that - “born of woman, born under the Law.”
When Jesus says, “No man born of woman has arisen that is greater than he,” Jesus is not including Himself – because you don’t ever include yourself when you’re giving a spoken judgment about history! It would sound really egotistical if you did. Welcome to good rhetorical practice! Also, He’s not strictly speaking a professional prophet, although He does prophesy. He’s God and the Messiah by profession.
He doesn’t say that John is the greatest prophet, mind you. He just says that none of the other prophets are greater than him. So it does leave the possibility that Elijah, Moses, Jeremiah, etc. are equally as great as John, although that’s not normally how tradition has taken it.
And it doesn’t mention Mary, because Jesus is talking about “all the prophets,” when he’s talking about “gennetois gynaikon” (male-plural of “born of woman”, which can include women in the typical Indo-European way, but doesn’t have to). It’s true that Mary does act as a prophet on some occasions (namely the Visitation and the Wedding at Cana), but it’s not her profession like John or Elijah or Anna’s. Also, it was considered really bad manners to talk about a living woman in public and mention her name (unless you had to), so He wouldn’t have said “except my mom Mary, she’s really awesome.”
Really, if you’re going to worry about a text in this passage, “John is Elijah if you can accept it” is a lot more weird.