I find it funny how the tension between tanks and healers is still ongoing. That aside, I can heal as well as tank so I know both sides of the argument.
In my opinion, the healer should try to evaluate the situation and instead of punishing a bad tank, should try to adapt to their play style. It sounds as though I babysit the tanks, but I'm the type of person who makes sure that the party is functioning at 100%. After all, the healers' main job is to keep everyone healthy, and to DPS is second.
As a tank, I had to make a new habit of popping a CD for each pull and learned how to manage my CD rotation and mana usage. Tanks are usually the ones at the forefront and if they are new, they may not know the fight as well as the healer/ DPS, who get to observe all mechanics in the back.
Instead of complaining and looking through one perspective, know that people with mainly only tank classes require much experience in the field in order to know the fight inside out.