Why do people get in trouble for not wearing their seatbelts? Shouldn't their own safety be their own choice?

No. Your so-called "choice" actually affects everyone. Insurance rates are determined by risk factors, and one such factor is seat belt use. Personal Injury Protection (PIP) and Uninsured Motorist rates have increased as a direct result of failures to use seat belts. That hits my pocket. Therefore, your decision affects me.