An obsession is a persistent, intrusive thought that persons cannot seem to get out of their minds even when they want to eliminate it.
Sex addicts use their obsessions as ways to nurture themselves and to numb the emotional pain in their lives, so when it comes time to give up their obsessive thoughts, they feel like they are losing an important and valuable part of themselves.
Obsessions are important aspects of the addictive process, and most addicts spend much more time thinking about sex than they actually spend being sexual.
See also: Compulsion