What happens if your opponent activates right when you play to destroy monster?

When you play a monster to the field, your opponent has an opportunity to activate Quick-Play Spell Cards, Trap Cards, or monster effects that can negate or destroy your monster. If your opponent activates such an effect, it will resolve before your monster's effect can activate.

For example, if you play "Blue-Eyes White Dragon" to the field and your opponent activates "Lightning Strike", "Lightning Strike" will resolve first and destroy "Blue-Eyes White Dragon" before its effect can activate.

If your opponent activates an effect that targets your monster, such as "Dark Hole", you can chain an effect that negates the targeting effect, such as "Solemn Strike", to prevent your monster from being destroyed.

If your opponent activates a card that destroys all monsters, such as "Raigeki", you cannot chain any effects to prevent your monster from being destroyed.