Why do girls break up with guys then want to be friends then get back together?

Guys break up with girls and still want to be friends because of two main reasons: Either they really enjoyed your relationship before you began dating, and they would like to continue that; or they want to keep you around in case things change. I believe the first reason is the most common.

Breaking up is not the end of the world. You should be glad that they still want you in their life. Embrace it, and enjoy it.