Sam Winchester had a lot to make up for. He had allowed himself to be led down a twisted path by a demon, because of some warped emotion he had developed toward her, and had destroyed the last seal to start the Apocalypse.
How could one ever apologize for so a monumental, catastrophic mistake as that? Humanity, as dysfunctional, egotistical, judgmental, and territorial as it was, was going to all be destroyed because of him, unless he found a way to rectify the situation. There was only one way; and he knew that Dean was going to fight him tooth and nail on it.
His brother's key role in life for as long as he could remember was to protect him. Dean had even paid the ultimate sacrifice and sold his soul to a demon in order to bring him back to life, and endured torture beyond belief down in the trenches of hell, before Castiel had brought him back to the land of the living.
How could he do any less to save his brother, Bobby, Lisa, Ben, and the millions of other people who were all going to die if he didn't man up and do whatever was necessary to stop the world they all knew from being destroyed? This was the only way he knew to make up for the monumental mess he had made in believing in Ruby, and starting the ball rolling for the Apocalypse. He would gladly give his life so that others more worthy could continue to live theirs.