"Independent" doesn't exist (mentally, spiritually, physically etc)...
Humans don't exist without Humans...
You're never "Independent" and parents teach a bit of a flawed meaning even taking it's best sides... which might be nicer version which is put raw "just get money any which way you can and we will respect you" type of "Independent" !
"More Independent" maybe works
but that is usually over-relying on other things (again connected to people or worse money which is debt to humans before even the human direct contact)