Ah! Moonrise, sunrise.
Please educate me then (no sarcasm here). While it might sound like unnecessary hairsplitting, I am trying to learn something, so bear with me.
I've been under impression so far that, at fool moon, sunset coincides with moonrise, thus sunrise with moonset. While, as you said, "everything rises in the east and sets in the west," it happens at different times of day, thus again, when sun rises in the east, moon sets in the west, and vice versa.