Your reasoning is invalid.

For your claim to be true, it would need to be provably impossible to explain human behavior with mathematics.

For that to be true, humans would need to be able to compute functions that are computable but outside the Turing computable, outside the set of lambda functions, and outside the set of generally recursive functions (the tree are computationally equivalent).

We know of no such function. We don't know how to construct such a function. We don't know how it would be possible to model such a function with known physics.

It's an extraordinary claim, with no evidence behind it.

The only evidence needed would be a single example of a function we can compute outside the Turing computable set, which would seem to make the lack of such evidence make it rather improbably.

It could still be true, just like there could truly be a teapot in orbit between Earth and Mars. I'm nt holding my breath.