The trap you are both falling into is the thought that political discussions centre around trying to understand the other persons point of view. It is almost always the other way around, one person trying to persuade an unwilling party that they are wrong. So as the poster said, as right as you are, you would still lose the political argument if that was how you tried to argue for your view.

You can be correct all day long and change nothing, or you can be persuasive and meet them in their thought bubble to coerce them toward aligning with your views. You can't just pop their world view with statements of fact, because they may very well think your fact is wrong. In this case not everyone believes the death penalty is immoral, so if your only argument is "the death penalty is immoral" you will change nothing.