He has admitted he never told his wife about the money given to Ms. White.
None of us know why Mr. Cain didn't tell his wife any more then you know why he didn't tell her. All we can do is speculate.
But if he was acting in his capacity as a assistant minister or what ever, it isn't anyone's business, including his wife why he gave that woman any money.
Do you want your minister telling everyone he knows the private details of your life with his wife?
That's something I would like to know. How many here would want their minister in their church putting their private business in the streets?