Since my point obviously flew straight over your head: the problem is not whether we understand monoids, or even that "Harry" used monoids to solve the problem, but that he's using completely inappropriate terminology to try to explain his solution to non-technical people.
Actually, he's using completely appropriate terminology. Your mathematical education is just sufficiently limited that you don't know that. Rather than getting angry, you'd think your reaction would be to absorb the new information.
To me, your complaint is like someone saying it's inappropriate terminology to discuss time complexity in big-Oh notation, because we're programmers, not mathematicians.
