My dad says that he doesn't trust me because I didn't tell him I got in trouble at school the Friday before my birthday weekend... but it wasn't even that, I wasn't thinking about it at the time because I mean it was my b-day and no normal person would, but how can I show and prove him that he's wrong??

Let me see, you got into trouble, did not tell him ( and of course he will think that it was because you did not want anything abouit your birthday to be stopped or charged or something?

And of course you say it is not because of that, but that you were just too busy to remember to tell him.

I don't think I would put that up for a vote here or anywhere,

And you are not going to win by trying to prove he is wrong, he has lost trust in you, plain and simple, fighting with him over it only makes it worst.

What you do is though time prove you can be trusted.