I'm frustrated at a friend for not helping me in a game
What kind of game was it? And is there another way to solve this?
I don't like to talk about this with him because he's such a bad loser.
It's good to help your friends out, but you shouldn't expect it from them all of the time.  Your friend might just take games too seriously, so you shouldn't get upset at him for the way he plays.  Maybe find a less competitive activity that you can both enjoy.
Maybe I just want to prove him how mad a player I am.
It's important to avoid falling into the habit of using your friends by always requesting their help.  Instead, you should appreciate the times your friend did help you and think about how you can reciprocate that help.