For instance, a business man might be cold and hard in his demeanor, but really enjoys watching childish cartoons. Or an exercise buff might also really enjoy deep fried chicken. It also might be a two word phrase, but I'm not entirely sure.
That's a guilty pleasure. Anything you're half-ashamed of liking, especially because it seems incongruous with the rest of your life (as those examples), or because society as a whole sort of disapproves (like eating a lot of chocolate ice cream).
Taboo ta·boo /təˈbo͞o,taˈbo͞o/ –Google
a social or religious custom prohibiting or forbidding discussion of a particular practice or forbidding association with a particular person, place, or thing.
"the taboo against healing on the Sabbath"
a social practice that is prohibited or restricted.
"speaking about sex is a taboo in his country"
prohibited or restricted by social custom.
"sex was a taboo subject"
It is taboo to ask people of which debaucheries they partake.
Edit: In my haste, I didn't even mention the word embarrassment, which I skipped over to go right to the cause of it. Some people think knowledge of their vices might "ostracize [them] from society" so they'd rather not "mention them" and therefore (personally) consider the topic taboo.