I know that growth comes from genetics, but I want to know what things stunt the human growth during the time it is developing in peberty.

Clicking on the following search may be something that you might want to try.

Human Growth Stunting During Puberty - Google Search (http://www.google.com/search?hl=en&safe=off&q=Human+Growth+Stunting+During+Puberty)

On that search, you will find a number of possibilities as to what might stunt growth during puberty.

Bad nutrition, too little sleep, exposure to artificial hormones such as steroids, some drugs, a traumatic accident/broken bones, severe infections, eating disorders, problems abosorbing food (ie Chrone's), they are all the ones I can think of at the moment.

You are right to mention human height is a mixture of nature vs nurture. That is why in recent history people have been getting taller than their fathers and it is mostly to do with better nutrition.

I remember one school that I taught at that was a private one. Most of the kids were much bigger than average for their age. They came from overall, very affluent families.

At a couple of other inner-city schools where I taught, children of the same age as the ones at the private school tended to not be so large. I was kind of shocked at the difference. So, maybe economic factors cold also come into play as far as contributing factors to the stunting of growth during puberty? Maybe economic factors could be one of the links in the chain of events/circumstances that leads to the possibility of stunted growth because of the nutrition not being as good in the inner-city diets because of the inability to eat more nutritious food because of not being able to afford it? Just a thought to consider...

I truly believe that is the case.

America's average height has slowed and actually declined recently compaired with Europe with the prevelence of fast food causing nutrionally poor diets despite relative affluence to the past.
Underperformance in affluence: the remarkable relative decline in American heights in the second half of the 20th-century (http://ideas.repec.org/p/lmu/muenec/1241.html)
It seems deprived communities are shorter.