I get he was a bit of a g1t in stymying her career at HHM, but she is more anti Howard than Jimmy/Saul is... who has many more reasons for disliking Howard.
when he demoted her to doc review she realized that he would never see her as an equal. When Howard try to explain to her about Jimmy being a bad influence it was very condescending. Also, as Howard said to her during the confrontation and when Kim told Jimmy a lot of what they did was just for the thrill of it.
Yeah, that's the thing - it's not even that she hates Howard, he's just a convenient target for their increasingly sick ploys. And Jimmy specifically uses him as a type of punching bag, to offload the grief/regret he has toward Chuck.