You are right about the argument in itself. It is poor. But the argument is not in meat of the argument, but in optics. The perception of things as 'rules for me but not for thee' almost immediately overrules even basic logic. In other words, make pain even across the board and people might listen.

You're speaking from the perspective of someone for whom the virtue of making personal sacrifices for environmental reasons is already obvious. Try putting yourself in the shoes of someone who doubts this. To those people, rich jetset climate activists come across like politicians who agitate against gay people then get caught having anonymous gay sex in airport bathrooms. Their hypocrisy is seen to invalidate the authenticity of their message.