There's really not as much of a logical connection between the two as you think. Replace "fly on a private jet" with any other rich person activity and your sentence still works. So it's not really about flying on a jet.

Did you hear what I said at all? Yes, if you are a capitalist who believes in capitalism, you aren't hypocritical for doing that. It's not a position I agree with, but it's a consistent position, as far as it goes. As long as you pay for your emissions / compensate the rest of the world in the ways we have agreed to, you're in the clear. Someone will take up the slack for you, in return for payment.

(Those ways of compensation may objectively be pathetically inadequate, but so what? It was "voluntary" so it's good enough. That's how it works for everything else things in capitalism, so of course that's how it's going to be that way for emissions as well.)