Words are inadequate

Part of it is that Toph's character arc is starting out in a very different place than that of the other characters- they came into their journeys through tragedies, whereas she's the only one that has truly chosen to join the group, and had a viable alternative. The option of choice is a vital one to her, and I don't think she's ever learned how to have both freedom and interaction with people; her sense of freedom, up to that point, was specifically tied to being hidden and concealed. It's how she learned earthbending and it's how she gained prowess as the blind bandit. So her journey in the story isn't like anyone else's. For her, a lot of it is learning about how to be part of a group, including learning how to let people close, how to be known without it making her less herself, and how to truly tie her fortune in to that of other people.

Of course, I could be entirely wrong, but that's what I got from her, and one of the reasons I like her. Your mileage may, of course, vary.

(don't forget escape from the spirit world as a short between seasons 2 and 3)