Being strong enough to lean on others without losing our ability to stand on our own is interdependence. This is not a sign of weakness to fight against - it's a sign of personal growth. Small children are dependent. If they want to eat they need someone to fix their food and feed them. When we get older and can feed ourselves we need to let everyone know that being fed is a sign of dependence and we will not allow anyone else to feed us.
Independence is good.
At some point we should realize that everyone knows we can feed ourselves, we no longer need to get upset when someone offers to fix our meals. They know we can do it, but they enjoy doing it for us. When you get to the point that you understand that you are independent - you don't have to prove it anymore. You can allow your independent self to be assisted by other independent people. It's a sign of strength - not weakness.