Why would you voluntarily go into counseling and not tell your therapist the whole truth?

When I entered marriage counseling with my wife, I told her all that I had been doing. Our therapist said that he believed that if there was infidelity, the person had to come clean or trust could never be rebuilt. There is no building trust on shifting sands.

I know other people who have told me that they hide things from their therapist. I’m not sure why. What is the point? You’re paying through the nose for some person to try to help you figure out what you want to do, and that person has no idea what you are doing?

Why? Why would you do that? Can you get anything useful out of therapy if you don’t tell the whole story?