Most parents are terrified of kids lifting weights or even training at a gym.

The concerns:
*Any kind of loading will damage bones 
*Any kind of loading will hamper growth

All bones are constantly getting rebuilt. One of the key stimulus for rebuilding: Compression through activity under the auspices of earth’s gravity. Astronauts lose 20 percent of their bone mass since they operate in the absence of gravity and the compression it produces. This means weaker bones. 

All human activity produces compression of the skeletal system. This compression is a crucial stimulus for bones to get denser and healthier. Lifting weights, jumping and higher impact activity produces more stimulus for denser bones.

Kids and adults both need compression for healthy bones. Kids adapt and reflect the physical stimulus they are subject to since they are rapidly growing and building tissue. 

The only kind of damage that can be counterproductive is damage to the end of bones. Regions called epiphyseal plates. This is where bone growth happens. To quote Breeland, Sinkler & Menezes:

-While bone is replacing cartilage in the diaphysis, cartilage continues to proliferate at the ends of the bone, increasing bone length. These proliferative areas become the epiphyseal plates (physeal plates/growth plates), which provide longitudinal growth of bones after birth and into early adulthood.-

Lifting weights, sport and plyometric activity is not detrimental to epiphyseal plates. But what can damage growth according to the Mayo Clinic:

-If a fracture goes through a growth plate, it can result in a shorter or crooked limb. A growth plate fracture affects the layer of growing tissue near the ends of a child's bones. Growth plates are the softest and weakest sections of the skeleton — sometimes even weaker than surrounding ligaments and tendons.-

Kids don’t fulfil their growth potential or could have less than optimal growth outcomes when they damage their growth plate. The more obvious and common reason for not fulfilling growth potential: Malnourishment. Not enough calories, protein, Omega 3 and other micronutrients as they grow up. 

TAKEAWAY
*Kids and adults need activity that produces compression. Compression is necessary to healthy bone development. 
*Depriving them of random activity and a systematic exercise program deprives them of the necessary stimulus during crucial growth years. 
*Protein intake, calcium, Vitamin D, Omega 3 are among the crucial nutrients kids need along with sufficient activity and calories to produce strong healthy bones, joints and muscle. 
*If you want to produce an adult with high basal metabolic rate and be able to sustain high levels of activity and strength, your best bet is to lay down the habits, bone and muscle early in life. It is impossible to produce the same results later in life.

In summary kids need to play, run, climb and some systematic training can enhance their ability to do the first 3 things.