Destruction of Destiny isn't guaranteed to deal damage, so you can't use it on that, either. (Or other cards that aren't guaranteed to, like Time Wizard or Dicephoon.)
actually, BBtD should work even against the effect of an already face-up card, it just needs the effect to be an ACTIVATED one.
Some cards have ruling that says the part of their effect that inflicts damage to you is not considered an activated effect (and therefore does not start a Chain). These cards' damage cannot be chained with BBtD.
It doesn't work with cards you control, phew. Tried destruction of destiny, burning land and Axe of fools. Is counter trap only usable against opponent cards?
It doesn't work against cards that aren't guaranteed to burn (Destruction of Destiny) or Spell/Trap effects, only their activations. The latter's typical of Counter Traps in general.
Spell of Pain works on Spell/Trap effects like Burning Land's because it's not a Counter Trap. (Still won't work on a card like Destruction of Destiny that isn't guaranteed to inflict damage, though.)
To prove my point that it's not because you were trying to counter your own card effects, it'll work on a card like Memory of an Adversary or Supremacy Berry.
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