The fact is that, as an adult, you can't keep depending on other people. You should be thinking of being absolutely independent.

Can't agree here. An adult can't afford to stay independent for too long. There are 3 stages of maturity: dependence (when you are a child), independence (when you just became an adult) and Interdependence (when you are ready to be a team player and build your own family). So to really grow up and became a fully functioning adult, you need to learn to gave up part of your independence and learn to depend on other people again.