I have known this man for 3 months. We have become very close and he states he has shared things with me that he has never told anyone. He has a history of numerous relationships that he has walked out on and never looked back. He has never attempted any physical closeness except for a hug. I told him I craved his touch the other day and he said he was not going to do that. After I left, he called and left a voicemail on my phone saying that was the hardest thing he had ever said in his life. What should I conclude?

You should conclude that he values the friendship and doesn't want to mess it up by getting into anything with you.

You should conclude that he wants a friendship with you, not a love life.

Maybe he just needs time

he values your friendship and don't want to mess that up

It sounds like he quickly walks out on women once he has sex with them.
Next step might be to ask him. We can guess until we are blue in the face.

I would question why you want to have sex with your best friend. For a myriad of reasons - even if you take morality off the list entirely - it's not a good idea to have sex with someone unless you are in a committed, loving relationship with that person.

If you are attracted to him in that way, I would suggest you continue the friendship and respect his decision. Let him know you would be interested in dating him down the line. But if he's working on his track record and trying to change his character it can only benefit you to permit him to finish doing that before you get physically involved with him.