I have literally never heard a man use this phrase. The very phrasing suggests the speaker has a uterus.

Exactly. The phrase isn't "I want you to have my babies", which would indeed be a deeply creepy thing to say, and is something no one actually says.

She's saying now that people are focusing too much on that one example, but it's the only example she gave. A blog post probably would have been a better forum than Twitter for that particular rant.