Speaking as someone who has a lot of experience with people who don't apologize in their immediate family, apologies do one thing and do it well. They de-escala

Speaking as someone who has a lot of experience with people who don't apologize in their immediate family, apologies do one thing and do it well. They de-escalate situations in which honest mistakes have been made, and decrease resentment over time for those mistakes. People who don't apologize create the impression that they don't actually care about other peoples' feelings, and guess what: we notice that.