I agreed with you until the last paragraph, where it seems to me like you just fell into the trap you were warning us about. Not sure if that was your intention, but that's what it looks like.

The first part is definitely true though. Calling somebody an idiot is probably one of the worst ways to get them to agree with you, even if they are spouting idiocy. I won't pretend I have a solution to anti-vax beliefs, but simply calling them stupid won't make them disappear.