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Armor-Piercing Question and Armor-Piercing Response for the "serious statement that halts someone in their tracks" part
Cryptic Conversation and its subtropes for intentionally confusing someone to make them think or avoid giving a direct answer.
Break Them by Talking is a more weaponized form of the concept. Distracting someone with total nonsense can also be part of I Shall Taunt You and Confusion Fu.
In extreme cases, this crosses into Brown Note- a statement or question that can simply shatter the person's mind.
Edited by Scorpion451
I Shall Taunt You if it's an insult that discombobulates or angers the other party.
How about cases like this?
- One Piece: During the Straw Hat Pirates' fight against Big Mom, she points out to Brook that his soul-affecting Devil Fruit abilities doesn't work on her. He agrees, and then goes to say his memetic line: "But at least... can you show me your panties?" This causes everyone to get confused (or "lolwut" as I would call it) for a brief moment, but enough for Brook to make an opening to attack the living cloud she's standing on.
Edit: On a second thought, disregard that :)
Edited by Asherinka
This is similar to a logic bomb, but rather with an artificial intelligence it involves a human being. More specifically it's where someone says something that confuses someone. It can be either comedic where the protagonist says something confusing to someone in an attempt to distract them, or taken seriously such as something that causes someone to question their actions, thereby causing an openning for a discration.