<human>: Me and my boyfriend have been discussing this. I want know what the right thing to do is despite the feelings. 

I want to be friends with my ex. This ex is not interested in being friends, he only wants to convince me to try again. I think there's a chance to get through to him and become friends, only its a small chance. I want to take it, but it hurts my boyfriend and he argues that for such a small chance it logically shouldn't be worth his guaranteed suffering if i pursue this. He is not giving me any ultimatums or anything.
 
I just want to know what the right thing in this situation is, logically.  
I also find it unfair because my boyfriend will guaranteed be friends with his ex who hes been in a 5 year relationship in. We only dated for a month so far. 

So which of us is right?

Condense the text into a few key points
<bot>: My boyfriend thinks its a bad idea to be friends with my ex because this ex is only interested in getting me back. But i value him as a person and wanna try keeping him as a friend. Am i or my boyfriend right?