Personally independance to me means being able to choose to do things, or not do things. I have chosen to be financially dependant on my husband currently. I have chosen to live rurally, with my nearest neighbor a mile away and a stranger to me rather than live in a subdivision with people only yards away, there if you need them. I have chosen, reluctantly, to live away from my family, because I chose to work in a field that had few jobs in the area my family lives. I have not decided if I will homeschool or not.
Independance also means responsibility. You are free to choose but you also have to step up take responsibilty for the results of your choices. The fact that I have no babysitter is the direct result of where I choose to live & the price of my independance from nosy neighbors & interfering relatives. I can't blame anyone for that but myself. When you are young & your think about being an independant adult you mostly think about the power, I can stay out all night, I can eat whatever I want, watch whatever I want, wear whatever I want, etc. But you don't think about the responsiblity that goes with it - you have to get up & go to work at 8am after staying out until 5am. And if you are late for work then there won't be any money for the food, the clothes & the movies. And while you are free to choose your food & clothes, eating nothing but sweets will make you sick and so will wearing shorts & a tank top out in 30 degree weather. Yes, you can do whatever you want, but you will also reap the consequences of those choices. It's not all fun & games being independant. Lots of people fail to notice that until it is too late & then they go looking for others to blame rather than accept the responsibility of their choices.
You can't have one without the other.