Based on Persona's 3 character Yukari Takeba, the moment happens when a fictional (usually female character) acts aggressively torwards someone/something for no apparent reason.
Its quite similar to being a tsundere, however, without the motivation of jealousy that a Tsundere has.
Commonly happens with bad written anime characters.
"Man, why does Chie from Persona 4 have such unnecessary Yukari Moments?"
"I love Akihiko from Persona 3, he never had a Yukari Moment."
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