Most people are employees at will and have no employment contracts or union contracts that protect them. That means that a boss can fire them at will for any legal reason (that carves out such things such as race, color, creed, etc.) or no reason at all. If there is an employment contract, or a union, that's different.
Most bosses aren't stupid enough to do random firings as it can be horrible for morale. Also, most large companies have rules that their local managers are told to comply with, that are designed to prevent arbitrary firings as senior managements know that it is bad for business long term. But insubordination is always one ground that is open. You can comply or appeal to higher management, but my guess is that if push comes to shove, you'd be out, not the boss.
A boss has to look after the needs of the business first. If there is a real need for you to be there on what was a scheduled workday, and there is no real hardship or very strong reason why you couldn't shift your schedule once in a while (like you are getting married on the day the boss wants you to work, or attending an out of town event with non-refundable tickets) and you are unwilling to be flexible, you should be history. Make a case or look for another job.
