I think the core argument was wrong and it was surrounded by a whole list of other errors which demonstrate flawed thinking and lack of knowledge and understanding.

I further think that pointing out errors is absolutely vital and core to intelligent discourse and discussion. It is a terrible weakness of 202x attitudes that saying "you are wrong, your reasoning is wrong, and here I will spell out how and why" is perceived as rude.

This attitude is what led to Trump, notably the 2nd term, it led to Brexit, it led to the Ukraine war, and it led to international attitudes on Israel v Palestine.

Calling out mistakes and outright lies is crucially important. It is not rude or discourteous. It is necessary.

If people don't like it... well, tough.