They say it's been proven through mathematical methods.

The details are pretty dense, but to sum it up in one sentence, it's because Gödel's incompleteness theorems were applied.

The universe operates on laws that function even when incompleteness is present, but simulation theory is based on the idea of building the laws of the universe by stacking information through some algorithmic method—so they seem to clash. Since algorithms themselves can't transcend incompleteness, they can't mimic a universe that includes it. Basically, it's because the universe transcends algorithms.

It's one of those things that makes sense until you think about it too hard, so check the source for more info.