We, Students, should be able to wear hats while in class, at school, and just walking on campus without being constantly harassed, scolded, and sent to the principal's office for wearing an appropriate hat. If this petition were to succeed, students wouldn't be less confident in what they wear. The "No Hat" rule shows students that just because someone said so, they shouldn't wear something that they like that's appropriate.

The common thing said, "It causes a distraction" is full of bull, someone can wear light-up shoes, and a shirt with tons of glitter, and can be a distraction but they don't care. A simple ball cap won't affect anybody, sure it may be like "hey cool hat" for a couple of days but after everyone is used to it, it will be like wearing a mask, a sweatshirt, etc. 

Another positive is people who may not like their hair, get bullied because of their hair, etc. will be able to wear a hat and won't have to show their hair. This boosts their self-motivation, and confidence, and can stop some bullying. 

One thing that schools may state is that "We can't see your face" the only thing that is covered up from a hat is the top of your head which includes, hair and forehead. From behind the head, you wouldn't be able to see their face in the first place without a hat.