Since $P \subseteq NP$, if the statement is false, it cannot become true by changing $P$ to $NP$.
What your teacher is doing here is trying to illustrate a very common fallacy amongst beginning CS-learners. He is giving one potential way to solve a problem, and he notes that this way needs more resources than we want to make available (sometimes it is instead: involes a non-computable subroutine). However, this says nothing at all about the complexity of the problem. Maybe that algorithm is simply not a good algorithm for the problem. Since, as you should know, sorting can be done in (less than) quadratic time, indeed trying out all permutations is a very bad way to sort a list.
To actually show that a problem is hard we need instead to reason about all potential algorithms, which is very difficult. Thus, we usually just recycle previous impossibility results via reductions. Sorting, however, comes with an innate lower bound: As long as we are dealing with an "unstructured" data type only allowing pairwise comparison, we cannot do better than $O(n \log n)$ by an information-theoretic argument.