In response to the claims of sexual harassment he said "I have never acted inappropriately with anyone. Period."
I don't think there's a human alive who can honestly say that. Thank goodness! On the other hand, I'd be even more worried about him if the claim were true! That's just not healthy.
I have "acted inappropriately" with lots of people. I also enjoy it when others (particularly of the opposite sex) act "inappropriately" with me. But I guess it depends on what you consider "inappropriate". Maybe there are times "inappropriate" is appropriate.
Cain also shows a lack of understanding of reality in that he offers to take a lie detector test to "prove" he is telling the truth. Lie detector tests do not detect lies or verify truth. They are pseudo-science just like astrology and creationism. Or, maybe he knows this but is playing along to satisfy the dupes who support him.