Jack had sensed it the moment Dean had stepped into the room with Sam, the bond, the connection between the two. Dean was the alpha male who did look to Sam for his opinion and take on a matter but it was Dean Jack needed to prove himself to. That is why he started copying Dean to let him see that he could be just like him.
When Dean came to him and found him stabbing himself he could see the worry in his eyes and fear that he might hurt himself then Dean made his promise and Jack knew Dean would follow through.
Dean didn’t know why he told Jack what he did but part of him felt it was only right to warn the kid. He didn’t want any more blood on his hands but he knew he would do it if only to keep Sam from having to do it. Sam saw himself in Jack, he wanted Jack to see that he was more than just the son of Lucifer.
While he didn’t know the whole story Jack could feel that Sam’s soul was damaged and worst of all he could feel his father’s touch on it, screaming for him to stop. Jack didn’t want to know what that monster had done to harm a kind person, he didn’t want to be like that.
Jack might have been among the Winchester’s for only a little time but he had come to realize that Dean would put himself in harm’s way, he would be the first one to step in the line of fire to keep not just the world safe but more importantly to keep Sam safe. Sam is Dean’s whole world and to keep him from having to do anything that would hurt him Dean would take his place.
And if it did come to that Jack wanted it to be Dean to be the one to put an end to him if only to spare Sam in the short time he had been alive Jack found himself drawn to Sam and the last thing he wanted was to sully Sam’s hands.
Dean and Jack had one thing in common and that was they both cared about Sam and for now it was enough.