Everyone wants to feel needed. Look at relationships where one side is completely independent, as you say, or at least tries - they usually don't work because the other part feels like crap. They equate love with need.
I think most of us do, I mean, I know I do. You don't want to feel not needed, because that means you're easily replaceable, at least in your head.
Besides, a lot of our relationships are based on an exchange of sorts. I'm not saying you don't care about your friends/family, but they give you something - they listen to you, they give security, love, support.
And you give something in exchange. If you don't need anything from you, then all I'm left with is your love. And how reliable is that?
There is always a return. perhaps it is cause and effect as energy pushed one way will eventually meet resistance and form a relationship with something else. Maybe our relationships are the energy that drives us and without them our energy doesn't meet the resistance required to do something of value.