No, he is not overgeneralizing. He is outright lying.
Whether he is repeating lies that someone else fed him, lies that he told himself, or lies that he came up with because he does not want to believe the science behind the vaccine, or most likely lies that he came up with because he has some sort of broken, stupid fixation on controlling the bodies of women whether they like it or not, the under-lying point: he is lying.