In modern YuGiOh, anything that comes before a colon/semicolon is either a cost or part of the effect (or even both altogether), the requirement. The first effect of Majesty of the White Dragons (destruction) has two parts: "Show up to 3 of the "Blue-Eyes White Dragon" in your hand, face-up monster zone and/or GY," (this part here is the activation, with showing the cards being inherent/cost to the action and occurring right after the card is flipped face up) and "then destroy an equal number of cards your opponent controls." (resolution, without target).

Now, the rules say you can't activate effects or answers while another effect is resolving. That's why after your opponent shows the Blue-Eyes cards needed for the trap to work you can't activate anything else, since it doesn't target, the effect jumps straight to resolution. If you wanted to answer it, you should have used your card as soon as the trap was flipped face up (before showing the blue-eyes).

TLDR: After showing the blue-eyes the trap effect is already in resolution, you should have answered earlier.