Why does putting the leads of an ammeter in a receptacle short the outlet?
An ammeter needs to be connected in series with a circuit to test current, which sticking the leads in an outlet does not do?

It does. Your meter is in series with a circuit: power plant, a long cable, your meter, same length back to the power plant.

Also, there is no amperage to measure on an outlet with nothing plugged into the outlet to draw current, correct?

That would be correct, but:
You just plugged in the meter. That's a Short circuit. A huge current will flow.

Why does attaching the leads to each hole of the outlet short the outlet

Because an amperemeter is effectively a short. It's just a thick piece of wire with a sensor next to it.

and trip the breaker?

Because a huge current flows.