I personally believe that asking the details of why a person believes something is EXACTLY the right way to have a discussion because if you just scream at the person and say you're wrong, that person will just dig in and solidify his opinion.

Asking someone

So they should buy the house, pay the mortgage and let you stay there for free?

Is not an attempt at understanding why a person believes something. It's the passive aggressive equivalent to yelling at them that they're wrong.

I am not surprised in the slightest that when pushed to actually define and defend your stance you respond with

I'm not going to argue with you anymore