A choice function $f$ is defined on a collection $X$ of nonempty sets and $\forall A \in X $ we have $f(A)\in A$. So the Axiom of choice states that for any set $X$ of nonempty sets, there exists a choice function $f$ defined on $X$.
Could you please explain (with examples, if possible) why the Axiom of choice leads to non-constructive proofs?
Thank you for your help