WELL I SEEM TO BE SOME SORT OF CHALLENGED PERSON HERE. See: End of first paragraph

I have an air compressor that is 20 amps, and I need to be able to use it in an entirely 15 amp environment. My assumption on the compressor is that it has a constant draw of less than 15 amps, but an initial startup of more than that, resulting in the 20 amp requirement. Looking at the compressor again, it is rated at 230 VAC. Does this change anything?

From an entirely theoretical standpoint, using some custom cording and screw-on plug ends, one could make a sort of patch from a plug on breaker A to a separate plug on breaker B (both being 15 amp) and you would have a trip power of 30 amps, because of how wiring in parallel works, right? The compressor would draw an even amount of power (more or less because of wire resistance) from both lines. If something completely strange were to happen causing a fault on one breaker, that one would trip causing the other one to trip, and that would be all as far as I can see.

Different way of putting it. You have two batteries that both put out 15 amps and the correct voltage you need, but your device draw is 30 amps. Wiring the batteries in parallel would result in the same voltage but a source amperage of 30. (where my theory that this would work comes from)

If I did this, would it actually work or would I just start blowing breakers? I have ample wire gauge capacity, all of my plugs are correct, and this would only be temporary wherever the compressor was (plugged in and used for 10 hours or less, unplugged all other times.)

There is no way to electrically, physically or legally make this work.
Unfortunately your battery analogy does not apply with AC circuits like this.

I need reasons. Telling me that it won't work doesn't help me learn, although that does answer the question definitively

Sorry, you'll have to get a book or three on electrical wiring and codes, because I'm not writing one.

What you propose will violate several codes and safety standards. These can be found in the NEC and the UL White Book.

Just a couple of things. By code you are not allowed to parallel conductors under the size of 1/0.
Parallelling would increase capacity.
Also if you were to wire ends on cords, and 1 came unplugged, the prongs would be Live and can Hurt or Kill.
Fires are also a concern.
If this Motor can be wired for 120/240 volts, the current would be half at 240 volts.
If the wiring is #12 try a 2 pole 20 amp breaker.
What is on the Name plate? Current at 240 volts, both currents may be listed?
Just Get your Pair of #10's and a #10 ground, If needing 30 amps? It will meet code and be safe.

Instead of getting into the theoretical, can you tell us exactly what you have and what the issue is?