Here is how I see it:
There are a lot of players who are intolerant to mistakes. Unfortunately, everyone who plays is human, and mistakes are bound to happen. When the DPS isn't hitting as hard, it's difficult to notice. But when the Tank loses aggro or the Healer misses a heal, it's very apparent. With pressure to improve performance on the tank or healer role, it makes sense for anyone to get agitated and respond negatively. On the flip side, Tanks and Healers might get mad at DPS because they feel they've done something wrong. Most of the time it's a matter of inconvenience -- attacked a wrong mob or accidentally pulled a group and suddenly you're getting ignored.

But I disagree with the idea that the mentality stems from being a Tank. I think given the chance to choose different roles, they would have the same kind of personality.