That is a big flaw in his way of argument of being worthless. But how does he think it will continue? I think is an important question.

But let's flip the board around now.

Why would he say something like "you have worth but I have none" even when you state otherwise? You say he's using emotional reasons instead of logic, right? But if his argument is "you have things I do not", that is a logical argument. He's using objective facts even if he's being emotional about it.