Why should we apologize to people?

I thought of this question after reading another person’s question/answer on here.

If I say something that hurts someone else’s feelings, when is an apology called for? I know it’s never a definite that you have to; it’s always just an option that I choose. But in what circumstance would I choose to?

How they feel is a result of their thoughts and interpretations of what I said, so if they’re hurt about something I said, it’s never really my fault. Therefore it seems like apologies are only to make the other person feel better.

I could apologize so that the other person does feel better and feels like I care about them, but then it’s like I’m trying to control their emotions with my words/actions. I’m saying “sorry” so they’ll feel better. Or they want me to say sorry so THEY’LL feel better

Now that I write this, I’m thinking the opposite situation is also true. Why should I ever give someone a compliment? Obviously, they’re intended to have a positive effect on the person. But I can’t influence what other people think, and I have no control over that. Their thoughts and feelings are their own.

So why pay people compliments? Why apologize? What’s the point?

I’m just trying to get a deeper understanding of Brook’s teachings in these situations.