Well, if you really want to go this route, you can beat them at their own game and accuse them of Arguing From Fallacy. (A nice illustration: https://theupturnedmicroscope.com/comic/logical-fallacies-ar...)

That being said, I do think it’s important to avoid fallacious reasoning — it helps in making arguments clearer. As mentioned above, just because someone uses a fallacy doesn’t mean their conclusion is wrong, but it does mean that you can prove their argument wrong. (And any reply should ideally be phrased in these terms: ‘your argument has problem X’ is easier to respond to than ‘your argument has fallacy Y’.) Furthermore it means they are thinking less clearly than they perhaps should be.