I think some people’s self-worth relies on them being “good”/right/perfect, so they can’t apologize without also hurting themselves. I don’t really get it either, because in my experience being able to apologize when you need to, is a huge strength. People will overlook almost any mistake you’ve made when they know that you feel bad about it, instead of having it turn into an useless conflict.

Even if you don’t feel like apologizing surely you can say “I didn’t mean to hurt you and I’ll try not to do it again” or even “I didn’t mean to hurt you but I don’t really care about your feelings/I think you’re being unreasonable” so you know where they stand.