Is it called something when someone argues with false reasoning?

Question

Is it called something when people argue with nonsense or unreasonable reasoning? I'll try to give a specific example using a silly subject, a cupcake

We eat Cupcakes because they're tasty. Lets say one day we wake up and find that 1/5th of all people find cupcakes bitter and not tasty. Someone who is a fan of cupcakes might say "the reason why people eat cupcakes is for the sugar rush" which is obviously not true. Another person may say muffins don't suffer bitterness in 1/5th of people like cupcakes do so they should serve muffins instead. The fan might say but muffins can't be used to soothe cuts because it lacks icing; which is ridiculous thing to say because noone actually would use icing to treat a cut, we want cupcakes so we can eat them

Is there a name for the way the "fan" argues?

Answer 1

Although I agree with Weather Vane due to the simplicity of the proposed argument, I would still just call this "fan's" argument Fallacious, and I think this is what you were looking for: a way to describe invalid arguments. Fallacies are this sort of failure in logical reasoning, and although there's a whole lot of them you could specifically reference, the broad term non sequitur would work here, "where the conclusion does not logically follow the premise."

Answer 2

The argument is spurious

Cambridge
false and not what it appears to be, or (of reasons and judgments) based on something that has not been correctly understood and therefore false:

More forcefully, and particularly relevant to your question and example, Longman says:

Longman
a spurious statement, argument etc is not based on facts or good thinking and is likely to be incorrect
He demolished the Opposition’s spurious arguments.

spurious has more force than specious, which describes at least a semblance of logic, whereas spurious describes something that is just plain wrong:

Cambridge
seeming to be right or true, but really wrong or false:

spurious is similar to but not synonymous with fallacious, which has implications of false reasoning, even from correct facts:

Merriam Webster
an often plausible argument using false or invalid inference

So if the cupcake fan would listen long enough, you might say “Your silly cupcake arguments are fallacious because they are based on false logic, specious because they lead to the wrong conclusions, and worst of all are spurious because they are based on false facts”