Possibly Jesus was refering to tendency in humans to hang back with the old when faced with a new path, to be afraid to go the new way and stay in the comfort of the familiar ways. In other words, let those who have not twigged on the importance of the Christ, stay and bury the old man.
I would think that the young man was gaining awareness of his soul and the expansion in consciousness that came with it, which is why he was pondering following Jesus. I don't think anyone aware of their souls can possibly be dead to God, but I'm no master or messiah.
The Lord Jesus Christ taught that to enter the Kingdom you must be "born again". This new birth is the generation within a person's soul of a heart turned toward God rather than the one that is turned away from Him - the one we are born with. If you receive Jesus Christ as the Lord and Savior - believe HE suffered and died for your miserable soul, you are born again and you live a life of gratitude to Him for all He has done for you.
See JOhn 3:16-19