She made me stay after and write out an apology note to the class.
What was the reasoning that she expected this, and was it something that you ended up doing?
No. I blew it off and left.
I know that you don't think apologies are important, but not following your teacher's instructions to stay and write one was not a productive thing to do. Do what your teacher says, since she has your best interests at heart.
Okay mom.
I fell like the intent of  the teacher is just trying to teach you life lessons. Maybe talk to your teacher next time and apologize.  If something bothers you about the letter, share that with them and see what alternative measures you can take to make up for it.