I get the mixed feeling on whips, but really it should just a physical extension of you, enabling you to give an aid in a different place on the horse that your limbs wouldn't be able to reach. I don't feel bad about using a whip when it's really necessary, having said that I do not routinely carry one (unless it's horsefly or spider season).
Riding school horses are very rarely as responsive to the leg as a privately owned horse, they have to be a bit dead to it because otherwise they would react every time a novice rider accidentally gripped on, or kicked during a transition and that would cause a world of trouble. Also (and I mean no disrespect or judgement on you personally) novices are often inefficient in giving clear aids, a slight grip on the reins whilst trying to kick on a slow poke horse can be enough for them to choose to do nothing. The use of a whip can be a clear differentiation to a riding school horse that you do in fact mean to be giving the forward aids and aren't doing it by mistake.
Long story short, if you aren't happy with the way you are being taught, don't quit, find somewhere else that better suits your ideals, not all RS are made equal and some have different styles and methods.