Why do we hang on?

I have been dealing with feelings lately of why we hang on when people no longer want you in their lives...Do we hang on because we are scared to let go or do we hang on because we truly care about that person and their well being? It is hard to say..I have been very confused by this due to the fact I am such a caring person. What I am confused about most is do I continue to hang on because I care or do I let go to set that person free..If someone reads this and has been in this situation, I am open for opinions...because this one truly has me stumped.My heart is telling me to stay in and continue to care because that is who I am..Just do not know at this point...Life is always interesting.