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Tear Jerker: The World God Only Knows
The most heart-breaking way to end the series.
FLAG 68, which shows the painful reality of growing old. You have to watch as everyone you loved and grew up with pass away. While the loneliness in Rieko's heart remained, she was still glad she lived such a wonderful life, and carried on to raise her young grandchild.
FLAG 97, when Hinoki Kasuga under the power of her runaway spirit has grown to be a giant. Fiore pretends to be her younger sister, Kusunoki Kasuga, saying that she hates Hinoki, giving her a major Heroic BSOD. It was extremely heartbreaking especially we learned that Hinoki lived her life, trying to live up to her sister's expectations
The events in between FLAGs 166 and 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 her capture arc), 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 the entire 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.
... which has been taken to its absolute, bittersweet zenith via the last portion of episode 12 of the Goddesses Arcwith Chihiro having some flashbacks of those moments with Keima throughout the the last few episodes (including the kiss that she gave him), then with one last shot of her, clenching her guitar tightly, and slowly crying her heart out. (It even provided the page image for quite a long while until the reveal of the final two FLAGs.)
In relation to that, The Stinger of the preceding episode. Just hearing the claps of the people while the shot pans on the Maijima Festival concert stage... followed by Keima uttering his Catch Phrase as the title of the said episode is flashed on a white background. Doubly so for those who have read the Goddesses Arc portion of the manga in its entirety, seeing it as a Foregone Conclusion…
Just the third opening song, "Secrets of the Goddess", has garnered this reaction from quite a few people, not just because of the combination of harmonious choir, orchestral arrangements, and Haqua on vocals, but also the beautiful lyrics that accompany it. The song is divided into a prologue, six "chapters", and an epilogue, and is a summary of the whole Goddesses Arc. The "chapters" are named after each Goddess, the lyrics for each being about their hosts' personalities and/or character archetypes, with the exception of chapter II, which is written in Kanon's POV and is a Tear Jerker in its own right. The prologue and epilogue are both written in Keima's POV, but the true Tear Jerker in the song is the epilgoue, which summarizes Keima's feelings about the end of the Goddess Arc, including how much he regrets breaking Chihiro's heart.
Flag 250: Dokuro stays behind to deceive Vintage for the next 10 years, and she and Keima agree that even if they should meet again, they must pretend not to know each other. However, she promises she will always be there to watch over him. Then she puts on a certain black collar…
Flag 260. When Dokuro/Nikaido shouts out "Onii-chan!" to Keima in desperation after the time traveling device is destroyed... This troper really wanted to just reach out and give that poor lady a hug.
The end of Tenri's side of the story. Despite doing everything she did for Keima's sake, following his instructions to the proverbial and literal letter, all while pining for him for a decade, she and Keima do not end up together. In fact, she was painfully aware of the fact that she would not be loved back the entire time, since Keima had told her himself that he would never love her like she loved him, and wrote as much in the letter he gave her to remind her of this fact so that she would not get her hopes up. (Check the page image.) In spite of everything, Tenri did it all for him, holding that hopeless dream in her heart that something would change that would make him love her. Pretty much the only uplifting thing about this character's personal ending is that Diana promised to stay with them until they found happiness.
The simple fact the series ended. For a lot of people who've stuck with it after six years of serialization, getting to know and coming to love these characters, counting a lot of the stuff they've had to put up with, seeing a beloved series ending is simply painful. True, the series ending could probably not have been avoided thanks to Wakaki's condition, but no one likes watching something they like end. At the very least, Wakaki got to give his series the ending he wanted, instead of getting axed like a lot of manga do due to loss of popularity.