Can one "decrease" or "increase" sound volume?

Your daughter's English teacher is nuts. Sound volume certainly may be increased or decreased (as a non-countable mass noun). Possibly the teacher may be focusing on the setting on the volume control as distinct from the sound volume itself, but even if so that doesn't hold much water; even if the setting is a countable quantity, we still speak of those as being increased or decreased.

I really want to know the teacher's detailed reasoning behind this assertion, because it seems nonsensical as given.

Your daughter's English teacher could very easily open a dictionary and find that she's incorrect:

Turn something up 1 increase the volume or strength of sound, heat, etc., by turning a knob or switch on a device. 2 reveal or discover something : New Yorkers confidently expect the inquiry to turn up nothing. 3 shorten a garment by raising the hem.

Sound volume could also be refered to as the measure of the pressure generated by a sound in decibels. As the measured result of the actions turn up and turn down the synonyms increase and decrease make complete sense. I think that the teacher needs to re-evaluate their ability for critical reasoning.