Many statements in mathematics begin with "for all…" — they claim something is true in every case. To disprove such a statement you don't have to argue about every case. You just need one counterexample: a single case where it fails.

Take the claim "all prime numbers are odd". It sounds plausible — but it is false, because 2 is prime and even. That one case is enough to topple the whole claim.

Or take "n^2 > n for all n". Try n = 1: this gives 1 > 1, which is false. So the statement is false — one stubborn case is all it takes.