Can You Still Be Friends?

So I recently broke up with a man I really loved, but--it just wasn't going to work out, we wanted different things out of life, but it still hurt me none the less. I still wanted him somehow in my life, because he is such a great guy. Selfish move on my part...I know. But, in the past I have always been able to friends with an ex. Not like "hey, lets go get coffee!" kind of friends but a "If you got hit by a motorcycle I would still care" kind of friends. Today, the ex told me he can't do that, be friends with me. And it really hurt--I know I had to let him heal the way he wanted to heal, and whatever made it easier for him, is what he deserved, and what I want for him. But, on my side, I want him in my life, even if it's just as friends. And it hurts me to think he doesn't want the same thing. I don't know why he thinks we can't just be friends, I mean I can understand why not now. But I can't understand later on...

So I guess my question is, can you be friends with an ex? Or is it really just a selfish way to hold on to them. Like having your cake and eating it too?