Shaving does not make your hair grow back thicker, stronger, faster, or any other “er”. In fact, contrary to what parents the world over tend to tell their kids when their kids start shaving, it has been proven by numerous studies going all the way back to the 1920s that shaving has absolutely no effect whatsoever on your hair growth rate.
Hair growth is controlled by hair follicles found just underneath the skin. These follicles are not in any way affected by shaving. Only the outer part of your hair that is already dead is getting cut. The follicles underneath that determine thickness/color/growth rate remain completely unaffected by your shaving or not shaving.
How long back this myth has been widely thought to be true nobody knows; although, according to the New York Times, the myth has been popularly believed for at least 50 years.
One of the reasons people seem to believe this (beside just because their parents told them so) is that after they shave their hair and it starts to grow back, it seems much coarser or thicker even though it is not. If it were, inevitably everyone who shaves on a regular basis would eventually be covered in pencil-thick or bigger hair sprouting out of their bodies from every place they shave.
In fact, the reason behind this extra coarse feeling hair has nothing to do with it actually being thicker or anything of the sort. To see why it would feel coarser, think about holding a thin, long tree branch. When it is long, it will be somewhat flexible, allowing you to bend it a bit with little effort. However, if you cut that tree branch down to a few inches, you will no longer be able to bend it easily or possibly at all; it will suddenly seem much stiffer or stronger. The same type of thing is going on with your hair when you shave.
Some people also think it looks darker when it is growing back. This again is false and in fact why people believe this is a bigger mystery than the previously mentioned myth. If it were true, after a certain number of shaves, everybody’s hair would be black. There really is no reason to think it is getting darker, as once again, the hair follicles underneath your skin determine hair color and they are completely unaffected by shaving. It’s possible that people believe this, because, when they first start shaving, the hair tends to be quite a bit lighter than years later as they grow to adult hood. So perhaps they think this because through their pubescent years the hair darkens a bit naturally and so they think it’s because of the shaving when in fact the two have absolutely nothing to do with one another.
As far as the growth rate misconception, this more or less comes to the same thing. The hair follicles underneath the skin control it, so cutting away dead hair, isn’t going to do anything. People again likely think this one is true because when they first start shaving when they are young, their hair doesn’t grow that fast. Then as they become an adult, it grows much faster than it did when it first started popping up on their bodies. So they might misconstrue this to have been caused by shaving (and probably just like the previous one, backed up likely by their parents at some point when they first started shaving telling them that shaving will make their hair grow back thicker/darker/faster). But in the end, this line of reasoning is kind of like thinking the sun comes up every day because your alarm goes off every day around the time it comes up.
Now with waxing it is possible to affect the thickness and other aspects of hair regrowth. However, it will never be the case that the hair will grow back thicker/darker/faster. In fact, by waxing you are damaging the hair follicles underneath the skin; over time as you wax more and more, the hair will grow back less and less and even sometimes will get lighter colored and thinner. So though waxing, unlike shaving, actually does affect your hair growth, it more or less affects it in the opposite way most people think shaving does.