Our main goal in raising children is to prepare them for life. When they are small, we must protect and care for them, provide for them, and even provide for their enjoyment and entertainment, but these are secondary, not primary goals. The purpose of childhood is to learn the skills, beliefs and morals of society, in order to be valuable, productive members as adults.
Teaching a teenager a craft therefore teaches them more than a skill; it promotes self-esteem and confidence, and shows them they have a place in adult society. Woodworking in particular does this, as it is perceived as an adult activity. Producing a tangible, useful, three-dimensional object promotes satisfaction as well. The Amish, for example, require children to leave school after eighth grade to learn a trade. They believe that occupational training keeps the teens out of trouble due to right attitude.
This same belief is reflected in many rural, agricultural areas. There is belief in the value of the socialization and orientation that happen while working with adults, and also the passing on of values and culture. For adults who work with teens, this is a chance to return to the tradition of passing their skills on to the next generation. And teens earn the respect of their parents. Since many adults no longer produce handcrafts themselves, often the parents turn to the teens for help doing projects.
Teens appreciate learning real life skills, need the challenge to continue developing, and can maybe turn their new knowledge into a way to make some money. With earning comes a new sense of responsibility, building on their strengths and recognizing their weaknesses. They appreciate the positive feedback they get from others and they get a chance to use that hand-eye coordination they've developed playing video games.
If a teenager is interested in carpentry, one easy and valuable first project is a pair of sawhorses; these become useful tools in the completion of many more projects. There are many websites with plans for this project.
Once they possess these sawhorses, teens will be able to construct other projects much easier. Be sure to take photos of the process, they will be proud to show off their photo essay of their woodworking project. They can then move on to bigger projects, such as redesigning their room. This would play right into the teens' need for control, and desire for independence and being cool.
They can even take their skills out into the community via volunteer work, such as Habitat for Humanity, all starting with a crafts project in woodworking.