What Morally Separates Suicide From Murder?

There is a long tradition of people who contend that suicide is not morally impermissible. Yet, I am not convinced. I have a simple question which I believe demonstrates the immorality of suicide. I have not yet received an answer from anyone I have asked. So I open this discourse up to you. The question is below; please feel free to share your thoughts.

Murder is immoral because it violates somebody’s right to life. My rights only extend to the point where your rights begin. So, when I use my rights to violate yours, it is immoral/unjust.

My question is why my rights are different. Why is it morally permissible for me to use my rights to violate my own? Why does my autonomy extend beyond my right to life (if it does)?