The answer, however, is quite simple. They continue to run, jump, skip, collide and maneuver on their own if provided the environment to do so. So, strength exercises can be a part of a child's activity routine provided they are included appropriately. Exercises and movements on or with any equipment should be based on teaching technique, form, and forming good habits, not strength development. Be sure that whoever is teaching the activity knows the correct form and how to teach it as well as provide effective feedback.
People often fail to realize that body weight is resistance.
Pushups using one's body weight can be more intense than a bench press using 2-5 lb weights. Encourage good form, consistent exercise and sport participation to help ensure continued participation throughout the life span. Physical development rather than age should be another factor that plays into the weight training plan. So if your child has interest in weight training or fitness type exercises, go ahead and let them join in. But keep them focused on learning a variety of exercise techniques, keep resistance minimal, and progress slowly as their body develops.