Wait! Don’t leave!
Teach comes from the Old English taecan, to demonstrate or point out, or to train or persuade. Yes, it was certainly a flexible word. It comes from the Proto Germanic taikijan, to show, and the Proto Indo European deik, also to show (as well as the origin word for diction). I know I throw the word interesting around a lot (I swear, I mean it!), but I’m going to do it again: interestingly, in Old English, taecan was not used to indicate teaching like a teacher would. It was used in that “show” way I mentioned above, rather than specifically for instruction. The word they used for that was laeran (before you ask, yes, that’s where learn comes from).
Tony Jebson’s page on the Origins of Old English
University of Texas at Austin Linguistic Research Center