There are two main situations where a card can be destroyed when its effect is activated:
1. "If this card is activated..." Cards with this phrasing in their activation conditions are destroyed if their activation is negated. This is the closest to the "False Activation" scenario you're describing. For example, a card that reads "If this card is activated, destroy all face-up monsters on the field." If its activation is negated, the card itself is destroyed.
2. "When this card is activated..." Cards with this phrasing have their effect negate the effect of the card that activated them. This is typically used for countering spells and traps. For example, a card that reads "When this card is activated, negate the activation of a Spell/Trap Card and destroy it." If the opposing player activates a Spell/Trap card and this card activates, the effect of the opposing card is negated, and the card itself is destroyed.
Important Notes:
* "False Activation" isn't a term in Yu-Gi-Oh.
* Card Text: The actual wording of the card effect is crucial.
* Counter Traps: Cards that say "When activated" often act as counter traps, negating and destroying the card they target.
Let me know if you have a specific card in mind, and I can help you understand its effect!