What does it mean to be independent?

I’m going to tell you a little about myself. Both of my parents are hardworking people, so they always come home late. That means when I was 10 years old and went to 5th grade I already had to do a lot at myself. My school was about 50 minutes away, my sport was 40 minutes away and my weekly piano lessons were 30 minutes away. I got a key for the house and a yearly bus ticket. Even when I was little I was very busy and it was hard to manage everything. I am happy my parents made me do this because that's how I got more independent.
In the US no one has to do anything like that, they are dependent on their parents. 16 year old teenagers even get treated like a “baby”, even me and I hate it. I have to ask if I’m allowed to go somewhere beforehand, so someone can pick me up. It feels like a play date back when I was in kindergarten... They took my independence from me!
My organization said you are going to go back to your home country and be an adult. But how am I supposed to mature to an adult if I don't get treated like one?
I'm realizing that everything they told me beforehand is wrong, but also right somehow. I would have never made friends if I wouldn't have overcome my weaker self and talk to people even if I don't know how to have a conservation in that strange new language. I found out I can survive by myself away from home with no one I really know around me.
Maybe realizing that I can be on my own means I am now really an independent person?

Bus in Hamburg. http://english.hamburg.de/contentblob/3639180/data/bild-public-transport.jpg

There are so many things changing in my life right now. Being an exchange student is harder than I expected. I live in a house with people I never met in my entire life before. My best friends aren't here to hang out with me every weekend. School is confusing and till now this isn't the best year of my entire life as people in Germany promised it to me. But I learned to appreciate things. Back in Germany I never realize how blessed I am having such a wonderful family. People that love me and would do any possible thing to make me happy and successful in life. I hated it that I had to eat dinner and breakfast every single day with my parents, now there isn't anything I miss more. I don't actually want to be here anymore, but I still am. Why am I still here then? Because I know after I was dealing with such problems in the age of 16 I can reach whatever goal I set to myself in life. I thought I would come here to study and improve my English skills, but I realize there are greater things I have to deal with than my language skills.