It's my best friend's birthday but I don't feel like saying happy birthday.
Why did you decide not to tell your best friend happy birthday?
Because I'm mad at them for something.
Since they are a close friend you should show them that you care about them. Wish them a happy birthday.
I am not having it. I don't have to be nice to them and I'm not going to change my mind.
I know you're mad at him right now, but choosing to not say happy birthday is not going resolve the issue. This will only cause more problems and I feel simple communication could resolve these problems.