I don't feel like apologizing to my father.
Why don't you want to apologize?
He's always so arrogant about it and he doesn't bother to apologize either.
Parents can be difficult and sometimes won't admit they are wrong but if you made a mistake or are wrong you should apologize. It might help the relationship and maybe they can learn from you.
I don't think it's wrong to not apologize to people. If they are rude, fuck em.
Even if you might be right it is good to apologize and try to keep the peace. If you have problems forgiving him you could talk to him and express how you feel about the situation.