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Tear Jerker: The World God Only Knows
The end of FLAG 166 and the beginning of chapter 167. After realizing Chihiro doesn't have a goddess, Keima needs to break things off as soon as possible. But he's so confused over her confession (he cannot understand why she would love him before the capture), that the only thing he can think to say is very harsh. Then it turns out Ayumi, the girl with the goddess, was watching, and he tries to get back on track...it doesn't work.
Ayumi: You're the worst, Katsuragi!
(she runs off)
Keima: Yes...I really am the worst.
Pretty much all of FLAG 189 was one huge tearjerker. Between the dramatic irony of Chihiro's cheerful proclamation at the beginning of the performance, her continuing to sing a song that was clearly about Keima, seeing her look upwards at the Goddesses and realizing that Keima was never really hers to begin with, Keima leaving the audience to go cry on a bench, and the last panel of just Chihiro, showing that she had spent pretty much the entire song holding back her tears.