At first every need from eating to well - you know - had to be taken care of by parents. That was the dependant stage. Over the years more independence occurs and it should. However, total independence is not the end goal. In fact total independence is a myth and would be very lonely and unrewarding. The real end game is something called interdependence. Interdependence involves an appropriate amount of independence mixed with a good healthy amount of dependence too.
God never intended for man to be alone. In fact He said that it wasn't good. From the start He gave man a woman. Later they became a family and eventually friendships occurred as well. All of these represent dependency. As your teens transition into less dependence on family and friends, don't make the mistake of trying to force them to become too independent, self reliant and proud or resistant to advice. Remember they still need parents for advice and wisdom, they'll need family for support and enjoyment, and they'll need teachers, friends, pastors and others too.
In addition, remember you need them as well. Let's face it, as we parents watch our kids grow up, we begin to realize that we need their love and friendship too. As they move into adulthood, we'll find that we need support from them, encouragement from them, talks with them and maybe even advice as they grow in their own relationship and walk with the Lord. No, we aren't talking about being a buddy and not being the authority in their lives when they are 15. We aren't talking about them needing to live in our basement until they are 27, but we are saying that we think an interdependence should be fostered as they move into their late teens and twenties.
Finally, I'd be wrong if I didn't remind you of a truth I am sure you know. Ultimately, our complete dependence is on God, our faithful loving friend. Strive for interdependence. Enjoy needing others and be someone people need especially when it comes to your kids.