They’re not going to be convinced

A good faith discussion is not about convincing another, but instead about having an open exchange of information.

They’re not going to be convinced when they’re already putting words in the opposition’s mouth.

They’re illustrating a point which you failed to engage with. In no way did it put words in your mouth. The fact that you choose to be insulted by the way they decided to illustrate that point rather than engage with them in good faith says a lot more about you.

To reiterate: You didn’t engage with their argument, but good try nonetheless. It’s nice to see you cling to a fallacy rather than engage in good-faith discussion of an argument clearly illustrated for you to relate to.
Do better.