@ODA1995,
I am thinking of his employment. It's regiment to the hilt, no room for anything but perfection, attention to detail.
It's possible that for some reason you may remind him of, him being told off, for instance for not making his bed right, simple things. There seems to be one person that is "like" a person to the extent that they tend to treat them bad.
You are an Adult, you stated sometimes he's the best Dad. One day, tell him, one day soon. "You know what? You have always been my Dad no matter what, I'm not perfect and I have no idea what you went through or saw but I love you and want you to know that".
Sometimes, it's "love" that conquers everything, you've nothing to loose. Perhaps he feels that you rebel, don't love him, perhaps he thinks you living at home instead of making it, he needs to give you tough love. Those that come from this background only know tough love.
So consider also what Chai said because she is making a point that can point to perhaps how he is thinking.
You also need to speak to your Mom. She is your Mom and sit down girl to girl and ask her to tell you why she accepts the way he speaks, why does he speak the way he speaks to you, what does she think you can do.
Also you don't question "why" she allows it? Why is that?