IIRC angels as genderless comes from the scholastics and St. Thomas Aquinas. They tried to reason out (guess, basically) a bunch of things about angels, and came up with them being detached, bodyless consciousnesses that exist at or around a point.

Hebrew, Greek and Latin all have grammatical gender, which must complicate any readings from the bible on the matter. Angels are described as either indistinguishable from humans or completely monstrous - in the case of the ophanim, more abstract or machine-like than animal, even. The fluffy winged person idea came after, and almost certainly was borrowed from Germanic and/or Persian paganism.

I wouldn't be surprised if the weird teacher wasn't totally alone in that cracked interpretation, but only because medieval monks can be weird, as well.