Quoting the Dog of Wisdom (who dispenses wisdom from the Wisdom Tooth): "If your ball is too big for your mouth, it isn't yours."
It's a good wisdom for tanks to remember. Only pull as much as you know you can hold and survive. Some tanks can chain pull every mob from the start to the last boss; and if they can hold the aggro and survive the hits, more power to them. But other tanks may only take it one pack at a time (which is substantially less stressful for healers, especially in AoE-poor groups (DRG-MNK is a horrible combo for big pulls)). Tanks should only pull what they feel comfortable pulling, and should be in really good communication with their healers. If there's a mishap on a pull, then the tank and the healer should both adjust some to prevent it happening again.
That said, I will agree that the tank in question here is a bad tank. They bit off more than they could chew, pulling more mobs than they could hold and survive. And then they blamed you for it, while clearly and demonstrably not knowing how enmity works in this game, and not anticipating the healing aggro you would generate to keep him up (probably a WoW refugee, since tanks there get aggro just for existing). Just remember OP, that you are the healer; you decide who lives or dies.