I believe the answer to your question can be one of two things...possibly a combination of both.
#1. As was mentioned before: He is consumed with guilt and wants to ease his conscience. He doesn't particularly care it if it hurts his wife, he just wants to ease his own burden. Otherwise, he would quit the affair and carry the load of self-loathing and evil doing alone...not hit his wife over the head with it by destroying her self-confidence & ego, and her love for him and often the marriage. Which brings us to #2.
#2. He wants a divorce and is too cowardly to ask for one. He is in hopes that by confessing, the wife will instigate the divorce.
Could be one - could be both. Or the third reason may apply, he is truly repentant and has realized how much he does love the wife and wishes to be up front and brutally honest with her. It is up to the wife to decide which reason fits the circumstances best.
#1. As was mentioned before: He is consumed with guilt and wants to ease his conscience. He doesn't particularly care it if it hurts his wife, he just wants to ease his own burden. Otherwise, he would quit the affair and carry the load of self-loathing and evil doing alone...not hit his wife over the head with it by destroying her self-confidence & ego, and her love for him and often the marriage. Which brings us to #2.
#2. He wants a divorce and is too cowardly to ask for one. He is in hopes that by confessing, the wife will instigate the divorce.
Could be one - could be both. Or the third reason may apply, he is truly repentant and has realized how much he does love the wife and wishes to be up front and brutally honest with her. It is up to the wife to decide which reason fits the circumstances best.