Why do guys always wanna play the "Let's be friends" card?

Honestly with me it's because I had a lot history of lashing out when I wasn't the one to leave the other party, and they left me instead.

So it started to become something of a goal to actually be able to maintain a friendship when a girl dumped me and hurt me in the process.

I wanted to change, and continuing to talk to them helped convince me I really was changing my vindictive patterns.