It was clear from his very first appearance that Jason has massive mummy issues, I always assumed his utter hatred for woman-abusers developed from those.
According to Batman #408, When Jason was 11-12 or younger, his mother fell ill and apparently could barely move anymore. Since his father wasn't around (murdered by Two-Face) and he had no sibling, little kid Jason had to provide for himself and for his sick mother, "finding her food and stuff... keeping her warm... and alive... long as [he] could". This lasted for about a year, then his mother finally died and he was left completely alone. When Batman found him, he was keeping a picture of his mother next to his "bed".
Even after his biological mother sold him to the Joker and had him beaten to near death, Jason still fought to save her life, and told her to leave him behind to die and just save herself.
So I wouldn't say that's something he has in common with Dick. Dick simply likes women just because he is such a nice guy. Jason feels extremely protective of women because he has issues.