Ringraziamo il coglionazzo comes from the world of Fantozzi, the Italian comedy series built around Ugo Fantozzi, a meek office accountant constantly humiliated by bosses, colleagues and everyday life. The billiards setting fits that universe, where a supposedly pleasant pastime quickly turns into another small defeat. Shared as a short soundboard clip, the phrase has survived because it packages a very Italian kind of sarcasm: formal gratitude used to dismiss someone whose stupidity has just ruined the moment.