Had something like this happen in Ifirt Hardmode.

Warrior jumps in, loses hate, Ifrit turns around and blasts the DPS. We go about healing them. Tank loses hate again, comes after the healers. Wipe. Then it's, Derp, didn't get a heal derp. When I explained he lost hate, his buddy chimed in and said he didn't. And I was like, dude, I watched it happen.

Paladin figures it out, so second attempt he just tanks it. But they are trading hate, getting hit by Ifrit at the same time. Hard for us to heal that. But we do. Warrior dies, I swiftcast raise him. Almost out of mana, but I played conservative. Second attempt we end up beating Ifrit. Paladin also interrupted all the eruptions.

He kind of apologized at the end. But this kind of stuff does happen. I've been pretty lucky, haven't been in bad groups, even when I was responsible for 4 wipes on normal Garuda. Maybe you want to play on Cactuar?