Jesus was aware that some of the religious leaders of His time were plotting to destroy Him. When we are rejected, hated, and threatened with murder, we normally turn in on ourselves and become preoccupied with our problems. However, Jesus did just the opposite. He reached out to many people and cured them all (Mt 12:16). When we're wounded, we think of being healed. When Jesus was wounded, He healed others.
When Jesus was hanging on the cross, He did not give in to self-pity. Rather, He kept forgiving those who were hurting Him (Lk 23:34), promised paradise to the good thief (Lk 23:43), called Mary to be a mother to His disciples (Jn 19:26-27), and commended His Spirit to His Father (Lk 23:46). Jesus was God-centered, other-centered, and even sinner-centered. Even in His agony and pain on Calvary, Jesus was not self-centered.
It's humanly impossible to die to self when you feel as if you're dying. However, Jesus lives in all those who have given their lives to Him. Christ will make us Christ-centered rather than self-centered. He will free us from the tyranny of self.