The difficulty is that there is an entire class of people who don't even care about being logically correct or in finding truth. They desire or "feel" something and will barge their way through to get it, even if it is antithetical to their stated goals and eventually results in their misery. Reasoning with such people is somewhat futile, even pointing out their fallacies in good faith will do nothing. They may even reject logic entirely, as is becoming more common in our society.
In that case, pointing out that someone is committing a fallacy can be something of a canary test of their desire to reason. You could offer to help them with their argument, point out ways around the fallacy, engage with them in good faith, but if they are obsessively attached to their fallacy and their flawed position, then there isn't much you can do. There is no mathematical or logical solution to that problem, that is a "people problem".
When dealing with such a person or class of people, using humour to make them look foolish can be more effective, since then the main goal should be to reveal to others how childish their position is or pressure them into abandoning their purely emotional position; or resorting to even better emotional fallacies. The name of the game is to get emotions on your side.