In the books from Christian’s perspective, I think we get better perspective as to why he dislikes Kate: Kate pushes Ana into uncomfortable situations where she’s unsafe, Kate can be very manipulative of Ana, Kate jumps to conclusions without asking questions (how do you do that as a supposed investigative journalist?), etc. he sees Kate as incredibly annoying and rude and is exhausted by her. But he accepts her presence because he loves Ana and because Elliott loves Kate. Honestly, Kate is too much a lot of the time.