I'm not sure that I understand your question or this mentality correctly, but I'll answer the best I can
From the age 13, I never considered myself depending on my parents except two points: I lived in the same home as them, and they made sure I could eat food every day.
But I paid for a new bed, new clothes, new television, new laptop, new cell phones etc. all by myself. Only if I needed something very expensive such as driver's license, they would pay.
I have had multiple jobs while underage, such as cleaning a pharmacy and working at a grocery. Because of this I could afford what I mentioned above.
In school, my father helped me with math until 4th or 5th grade. Afterwards, I was on my own. I had to learn language, history, social studies, biology, chemistry and physics all by myself. I had goals to enter university/college and adjusted my effort in elementary and high school to get the degrees necessary.
In taekwondo, I never had any significant support from my parents (mostly because it is non-sponsored here, but also otherwise). Every time I went to a tournament, all they said was "watch out for your head". And the only thing they wanted to know when I returned, was how it went (just the facts). When I had competed for 1 year and a half, I understood that my taekwondo journey was mine alone.
Since age 20, I have been on my own. Live in my own apartment and pay checks myself. Nobody's checking on me if I eat right, sleep right, study right, work right etc.
I believe that my parents' way of raising me is a little different from the ordinary. I have always been raised to take care of myself because nobody else will. They can't take care of me once I get old enough, my friends won't take care of me, my distant family won't either. Even though I live in a social democratic country, and the state can support me financially if I end up jobless, I personally believe the state won't help me get a job. Absolute egalitarianism doesn't not exist. Another way of understanding the point is that my parents gave birth to me, I was born in a society with certain laws and politics, yet I owe nothing to my parents or the society.
Additionally, their way of raising me taught me to do every thing for myself. Not for them, not for some guy, not for some girl, but me only.
I earn money for me
I study for me, and whatever course I choose, I choose it for me
I go to sport/work out for me
I eat for me
So by this analysis of myself, you should understand that
1: in order to become undependent on others such as your parents, you must do things that your parents do for you right now (e.g. parents support you financially, make you dinner - get a job and learn to cook)
2: you must do this journey of life for yourself, not for your parents or others
3: nobody owes you anything, and you don't owe anything to anyone. By this I don't mean that you don't owe your parents anything if you feel like it, but if you were a parent yourself you would probably do anything to support your child and expect nothing in return
I hope this makes sense, let me know what you think
cheers