The reason Yvain's proposed argument is arguably much worse is that the argument you propose is a clear, visible fallacy with spectacular failure modes and many people will indeed simply walk away or mark the person making the argument as crazy, while Yvain's argument, in the situations where it is the worst argument, is not only wrong and erroneous logic but also still manages to convince uninformed people that it is valid, and so they will accept its conclusion as true, while at the same time tricking opponents into debating the wrong points and formulating the wrong counter-arguments.

Yvain's WAitW is much more destructive, pervasive, memetically powerful, tricky to counter when there are large audiences and high stakes, and also much easier to do accidentally even when you know that it's a mistake - while pretty much anyone versed in the basic rules of causality and logic will understand and easily avoid the kind of arguments you've given an example of. Sure, some variants of what you describe, like "You heathens don't believe in God so any argument you make is invalid, only devouts of my religion can speak Truth!" can be pretty bad too, and this has been demonstrated, but it doesn't require as much mastery of logic to avoid committing.

As for what you can do, well... you could try to make them reasonable or rational, either through helping them achieve their existing goal of becoming more so, or through convincing them that they want to, or through other forms of manipulation... or you could always just do one of a plethora of other things you could do, like walking out, or learning physics, or killing them, or getting other people which this person considers as their Holy Authority to persuade them that they are wrong, etc. etc.

And there's always the sharpened bones of hufflepuffs.