A "gotcha button" is a conversational point which, when pressed, causes some substantial fraction of listeners to leap up and shout "Gotcha! That's obviously wrong and shows you don't know what you're talking about!", after which they have license to dismiss the conversation.
This behavior does not necessarily mean the listener is wrong. If you're describing your brilliant invention to a physics-literate person, and you mention that it can accelerate forward without pushing anything else in the opposite direction, the listener will shout "Gotcha! You can't violate Conservation of Momentum!" They'll be right, and their implied inference about your level of physics literacy will probably also be right.
Nonetheless, there are a lot of ideas that function as Gotcha Buttons for some significant fraction of various audiences, which do not correspond to a claimed known falsity.
Example of the first type: If you were explaining evolutionary biology to a novice audience, you might be wise to start with some example other than how hominids in particular evolved from primate ancestors. This isn't wrong, but a fraction of the audience thinks it's obviously wrong and diagnostic of you as someone they shouldn't listen to.
Example of the second type: If you were discussing Artificial General Intelligence, or AI with par-human performance in some domain, you might be wise to avoid the term "human-level AI"; because that particular phrase will cause some fraction of the audience to jump up and shout "Gotcha! AIs won't have a humanlike balance of abilities! There's no such thing as the human level!" (They can then dismiss the rest of your argument, without trying to carefully consider whether your further arguments are actually refuted by accepting "AIs won't have a humanlike balance of abilities", because you've made such an obvious and severe mistake that you just lose.)