You're being too vague for me to answer your question directly...
Indirectly, I am able to relate what I see:
I was born with the potential/birthright/nature to be a fully sentient being aware of myself and my world (IE the alleged 'outside' world) as connected to and interdependent with each other. I grew up in a society of semi-sentience where our awareness of ourselves and of our world is separate from the other (IE I am being myself over here, and everything that happens to me is out there).
The world does not 'happen' to me; though the choices and creations of others have been direct or indirect catalysts in my own life (Keyword: catalyst). Nor can I impose my own will upon the world (and likewise all its inhabitants); though my actions, behavior, and habits do act as a catalyst for 'the world' and others in their own lives.
Why does anyone want to "save the world's problems"?
Somewhere, they must believe that they are connected to and somehow responsible - even if in a small way - for the happenings and going ons in the world they percieve around them.
Why do they want to be considered part of the world?
While I can come from many different psychological standpoints (many that potentially or strongly agree with you), I would like to point out that this statement is... well, it's a Self-Detonating Statement! How can you effectively communicate to others in this world unless you are a part of it? IF you are not part of this world - simply put, you are not here... but here you are!
...However, I recognize I might be misunderstanding what you're truly getting at. If you would be so kind as to explain yourself or this concept in more than a single sentence it would be appreciated by more than just myself. ;-)