Will weight training stagnate growth in a teenager?
Is this a myth or fact? If it does, how does it stagnate a youth's growth?
The concern regarding stunting the growth of teenagers is related to injuring growth plates. It turns out that weight training does not increase the incidence of growth plate injury and does not stunt growth.
However, injury prevention requires correct form and the avoidance of overloading. It is especially important to supervise their training and teach form first. Crossfit Kids, for example, emphasizes form with very low weight (PVC only) until the student shows the emotional and physical maturity to use real weight. You can rely on an adult to make good decisions about their own limits, but the instructor should be making those decisions for a child.
Training improperly or with poor form will cause all sorts of injuries both acute and degenerative, whether one is a child, teenager or adult.
...but not really
That being said, the argument that lifting heavy things is itself somehow detrimental to growth is susceptible to a simple counterexample: children growing up on farms do all sorts of heavy lifting and their growth seems to be benefited, not stunted.
This Rippetoe and Pendlay interview has a layman's answer:
The Starting Strength book has detailed statistics comparing youth lifting to other sports in terms of injuries.
This article by Lon Kilgore goes more in-depth from a scientific perspective.