Why does the positive wave of my class AB amplifier output get clipped far below rail voltage?
I'm not sure why you AC-coupled your input and output, given that you have balanced power supplies, which makes it unnecessary.

The point that the commentors are making is that your bias network doesn't do what you think it does. You're assuming that the junction between the two emitters is close to zero volts with no signal. But in fact, the actual voltage is a function of the relative current gain of the two different transistor types.

Since the gain of an NPN transistor is typically significantly higher than the gain of a similar PNP, that junction is actually sitting quite close to the positive rail, even with no input. You need to fix your biasing scheme, possibly by employing some negative feedback at low frequencies/DC.

But just removing the input capacitor would also fix the problem, assuming that the source impedance is low enough.