There are two answers. First, American culture encourages everyone to think of herself or himself as a victim. The psychological advantage is that victims get to avoid taking responsibility for their own behavior and can instead simply blame it on the addiction. No one is a sinner today. People are simply victims of their addiction.
Addictions are often excuses for unacceptable behavior.
The second answer is deeper. Addiction is idolatry. Everyone who chooses something other than the Lord as the top priority in life is addicted to that idol. Addiction is so popular because idolatry is as popular today as it was in biblical times. This understanding of the problem suggests an effective response.