I think your reply overstates the importance of category theory in mathematics and doesn't give any hint on what it is about.

IMO a better reply would be: category theory appeared to unify the concepts around using discrete objects to prove the properties of continous objects in topology, like fundamental groups, homology groups and homothopy groups. It is only practically useful for very advanced proofs like 2nd Weil Conjecture. Any usage of it in programming is only an analogy and is not mathematically rigorous (see https://math.andrej.com/2016/08/06/hask-is-not-a-category/)