I'm mad and offended because my friend rejected my apology.
Do you think this will make you less likely to apologize in the future?
Yes, I will not say "Sorry" anymore. It seems some people don't care about the truth, only the offense.
I understand that you're upset, but you can't expect everyone to accept an apology every time. You did the right thing for apologizing and you should do the same in the future.
I'm still upset. Maybe I'm going to start cussing more.
Apologizing when you're wrong is important, but the other person isn't required to forgive you. Don't let this make you bitter or mean. Try to take the right action before you need to apologize.