I think coach class passengers look down on coach class passengers...hence why I've heard it called Monkey Class or whatever...
It also works in reverse....I've had coach passengers be difficult with me despite being very polite when I've tried to get to the Priority/FC line when they're just hanging back from the gate waiting for Group 8 or whatever but blocking the way..."Excuse me, are you in line for first class?" or similar
It's all out class warfare, I tell you!