Should I have kept my mouth closed? (speech, school)

[nature's message]

Okay, so most of this stuffed happened today at the end of the school day.

So a few days ago (I believe it was Tuesday), one of my friends told me that Ms. McLean (my geometry teacher) wrote me up for not wearing an ID. The thing is, I had my ID card with me, but the lanyard was at home. The ID was broken, and had I searched for the lanyard, I would have been late for school. None of the administrators called me up to their office, so I didn't think much of it.

Well in my 8th period class, one of them (Mr. Schmik) called me up to his office. When I was at his office, he just gave his speech about how simply wearing an ID was. I tried to give my side of the story, but he just cut me off. Then he proceeded to say "You're a sophomore. You should know that you need to wear your ID." As if I deliberately didn't wear it to **** off a teacher. So then he and I exchanged more comments. Honestly, his way of thinking just boggles my mind. I'm trying to give my side of the story, but he just continues to interrupt me, as if my (or any other students) opinions don't even matter. He then said "You're right, it doesn't matter. Because you are just a child, and she is the teacher." Clearly knowing that this was going nowhere, I said no more and signed the discipline slip. He gave me lunch detention for all of next week.

This was the first time I got really pissed off at him. This was the first time I got written up in while, and the only reason I get written up are for things that are so little that they should just be passable and overlooked. He makes me seem like I'm a bad apple, to which I'm not. I'm not trying to sound selfish, but I really think that he is making a big deal out of it. So, should have I shut my mouth about it?