In Batwoman's defense:
1. The first time I read your post, I also thought you meant he was only 4 years older than her.
2. Typically, in a case of murder, the spouse is the prime suspect, male or female. So Batwoman assuming the husband or fiance is guilty is less a symptom of "man hating" than a symptom of expecting the typical.
On the other hand, I think Batwoman is defining pedophile too broadly. I think it's less a question of a numerical age than a question of the victim's appearance, mental state, whatever.
For example: in NY, the age of consent is 17. In NJ it is (I think) 13 or 14. Does a 20 year old man in NJ "become" a pedophile when he cross the border in NYC simply b/c his 16 year old girlfriend went from being legal to not?
And, as noted above, years ago, it was very common for 13 or 14 year olds (or younger) to wed. Did that make all the men of that generation pedophiles? I doubt it.