I get mad at my friend(s) whenever they put themselves down.
Why does their self-deprecation bother you?
I don't have a reason. It just bugs me.
Even if you don't have a reason, you shouldn't just sit idly by when they put themselves down. They will feel worse the more they put themselves down.
I hate pessimism and seeing them hurt, it makes me feel bad.
It's great to empathize with others when they're suffering. If you really don't like it, then you should help boost their self-esteem by complimenting them and telling them they're wrong.