AC breakers are designed to support continuous current at 80 percent of rating, intermittent at rating, and overload for brief periods decreasing up to it's instantaneous trip rating (usually 5-10 times rated current). This is precisely because devices such as motors have very high starting currents.
For example, the 13KBTU air conditioner in my trailer has a measured starting current of around 40amps for about 0.5 seconds and settles to a run amperage of about 9amps. If the breaker tripped instantly at 15a, it would never start the ac, or almost any other appliance with a motor. A 15amp breaker with no other loads attached will support the ac just fine.
As a side note, this is why it is so hard to start an ac with a generator. When plugged in to a mains, there is as far as a RV is concerned unlimited reserve current capacity, so that 0.5 seconds at 40amp is supported. A generator however has no reserve capacity beyond what is stated. So if a generator is rated XXamps max surge, that is it. Exceed that number and the generator trips out. This is why we play so much with our acs in order to get starting current down.