Antarctica Starts Here.

Trapdoor goalposts - noun phrase - When two or more requirements are set up so that meeting one automatically means failing another. This is a bad faith argument whereby it is impossible to meet the requirements someone sets, without admitting refusal to allow the outcome the other person desires.

Example:
"If you're making a decent income you can't possibly talk about poverty, you don't know what you're talking about."
"I'm actually below the poverty line."
"You just want a handout!"