Suffixes: why do we say ‘accountANT’ but ‘teachER’ for different jobs?

Today, I was working with trainee English teachers on the CELTA course, when one of them asked the above question. Being a composite professional, I quickly told her that I didn’t know (but would find out, you know the drill).
It troubled me for the rest of the evening until I had a chance to look it up. The answer, as I had mumbled in the session before owning up, it to do with the derivation: ‘-er’ nouns derive from Latin  via Old English, which itself has Germanic roots, and forms the agentive noun. ‘-ent’ nouns (and ‘-ant nouns) came from Latin via French and refer to an agent in the service in the capacity of something.

Easy, when you have access to information…