My opponent played Wrath of Neos while I control Red Dragon Archfiend and Blue-Eyes Spirit Dragon. In response, I tribute BESD and special summoned Azure-Eyes Silver Dragon. Why does my monster still get destroyed from Wrath of Neos' effect?
since your opponent's activate Wrath of Neos=chain 1, your BESD'effect will be chain-2,so here will have a chain effect occurs. Besides that, Azure-Eyes Protection effect is a trigger effect, so you need to wait the chain effect resolves then after this protection effect.