Hypocritical singing is when a character sings a song saying he isn't going to/will never do something, but he does it/has done it anyway, or is doing it as we speak...I mean sing..
Related to and may overlap with Lyrical Dissonance.
"I'll Never Tell", in which Anya and Xander list all the secrets they're keeping from each other.
"Rest In Peace", in which Spike sings of wanting Buffy to leave him alone, but he wants the exact opposite of that.
Spike: (watching Buffy run like hell when the song ends) So...you're not staying, then?
"Poor Unfortunate Souls" from The Little Mermaid is a slight variation in that Ursula, while trying to get Ariel to make a deal with her, sings of how she [Ursula] uses her powers to help people. The song's hypocritical in that Ursula makes herself seem to come off in the very best light. While she does help people, she compares herself to a saint, but she also always has something to gain from her deals, and she goes out of her way to make sure that those under contract will fail to uphold their end of the bargain.
The Hobbit: When pressed to do Bilbo's dishes, the dwarves begin to sing about smashing his plates and destroying his property, while actually taking care to do no damage at all.
Meg's "I Won't Say I'm In Love" from Disney's Hercules
In Mary Poppins, Mary Poppins sings the kids to sleep with "Stay Awake".
In High School Musical 2, one of the characters sings about how he doesn't dance. Which is odd, considering that he was doing perfect choreography in the last movie.
Or in The Simpsons during the all-singing clip show when Homer says, 'Singing is the lowest form of communication." Marge says, 'But you sing all the time," and Homer replies, "No I don't, I hate to rhyme."
In Thenardier's song "Master of the House" from Les MisÚrables, he sings about what an honest and decent innkeeper he is, all while constantly cheating and conning everyone in the inn.
"Were you not to Ko-Ko plighted" from The Mikado. Many productions have Nanki-Poo and Yum-Yum punctuate "This, oh, this, is what I'll/he'll never do" with kisses. Pooh-Bah also has this line in "So Pardon Us": "To our prerogative we cling, So pardon us, So pardon us, If we decline to dance and sing, Tra la la la la la..." while dancing and singing.