Forum:Snipe Hunter chaining

During my opponents turn he declares activation of Snipe Hunter's effect, discards a card targeting my Face-Down Karma Cut. I chain with it, discarding a card to banish the Snipe Hunter. But opponent says he is allowed to keep activating Snipe Hunter's effect in chain, multiple times until he destroys all the cards he wants to or until he cannot pay the cost. Is he allowed to do that? He claims that he's seen it before (which i doubted at that time, and even now I still think he is lying) and claims that Snipe Hunter's effect is a trigger effect (which im sure it isn't).