What is a friend?

I have always been an all or nothing kind of girl when it comes to my friendships. Maybe I have too high of expectations of what a friend is? But, I always end up feeling silly for offering my desire to hang out or whatever after the 10th invite and no results.
What made me think that friends should be there for you and have the desire to be there? What made me this way? Maybe its because as I child I was let down a lot? My brothers would call (they are all a lot older than I) and say they were going to come get me to go out....and I would wait by the window for hours and they would never come (this isnt the case anymore as we are now adults). I love my brothers, but I felt let down on many occasions.
Maybe this is why I give so much to those I think are friends....cause I don't want them to feel like I don't care???
Someone recently told me that I make friends with people that I am so much better than.... that I sell myself short. But, what is wrong with caring about someone and wanting to help them out? I know that someone will only change if they have the desire to change....but what is so wrong with offering my 2 cents?
I am sorry about this post... I am just coming to the realization that my family are the ones that will always be there.... not a friend. My family will always support and love me, and I am so grateful for that...that I have a good family that cares.
I just need to let go, be myself and keep my family close.