I'm sorry you have had bad experience with big pulls, and I get it, it can be really stressful. Because if DPS is lacking, if tank doesn't use proper cool downs the blame goes straight to the healer. No one ever blames the DPS or tank they blame the healer. As others have mentioned you can tell the tank you don't like doing big pulls and in a perfect world they should accept that. I know that the big pull mentality is the "norm" but people need to realize not everyone is comfortable with that and it's okay to not like that. I myself sometimes like big pulls because it can be thrilling to take up the challenge that no matter what the skill or situation I'm gonna keep my party alive and it is quicker. Not everyone is like that and it's okay. Hopefully your future dungeon runs go better for you OP. Good Luck.