why do I have to work on a public holiday?

Just because it's a holiday doesn't necessarily mean all business comes to a halt. Not every business observes what many see as a holiday, and sometimes a holiday for some means that there is more of a need for workers in the service industry. (I chose service industry because most holidays mean travel, vacations, long weekends for many. That means more of a need for workers in food and lodging industries in particular.)

Not all employers give time off on public holidays and they make the rules, not you.

all emergency services...hospitals etc work...you know that when you go to work there..gas companies....elect companies....water services..may not have customer service for you to call but all are fully staffed for problems or danger

You have to. Not every company has the same policy.