While you did not mention your ages, I must assume that you are quite young and that this is one of your first major relationships?
Assuming this assumption is correct, I wonder if “everyone” you refer to is seeing something more, or different, in your girlfriend and your relationship with her (that is prompting their desire for you two to break up) than you are?
Having said that, there are two things that you mentioned that caught my attention: (1) “We both want something different out of our relationship.” And 2, “She’s dragging me down.”
Equally, I do not think that it is selfish or greedy of you to, “want to be independent, but still be with her”, or for you to “want her to grow up”.
In my opinion, when you combine these things with the behavior she displays, I am inclined to agree with “everyone” else … perhaps you two need to take a break and to date some other people. Based upon what you described, the two of you appear to be moving in opposite directions. What I mean by that is, generally speaking, people in happy and healthy relationships are motivated in the same direction with shared goals and values. It seems to me (based upon what you described) that neither of you is particularly happy in your relationship, but neither of you wants to be the one to breakup. Honestly, that is not a good reason to remain in a relationship. I think there’s a very good chance that there is someone out there who will encourage you to continue to grow and become the best independent person you can be — while making you feel like a million bucks, instead of bringing you down.