More accurately your job is to keep the group alive not necessarily every individual.
If a member of that group is acting in a way that endangers everyone sometimes the only option is to cut off a limb to save the patient if I can badly mix a few metaphors here.
Naw, Kipery - this is the *perfect* metaphor.
OP - one of the most important skills healers learn as they get better is how to identify when it's necessary to let someone die in order to prevent a wipe.
Order of healing priority:
If I die, no one else gets healed.
If I'm having to heal myself because I'm doing something that is getting me killed, then I need to attend to that first (ie... stop doing whatever it is that's causing me to take potentially lethal damage).
If I'm having to heal myself because something is trying to kill me, then I need to take whatever steps are necessary to prevent dying.
- Heal myself, pop defensive cooldowns (Barkskin, for you)
- Run to the tank and stand *ontop* of him
- Use any CC and/or interrupt abilities I have that may help the situation (Hibernate, Entangling Roots for you!) ... not all healers have good CC/interrupts, or whatever's killing you might not be affected by them, but try to remember to reach for them when things are going badly!
#2... The tank (or the pet, if the tank has died and the pet is now tanking)
#3... Smart dps'ers.
#4... Not smart dps'ers
#5... Pets (though if I have time to heal pets, I prefer to throw some dps out instead).
Sometimes, you just can't keep a tank alive. Maybe it was a terrible pull and the tank got overwhelmed; maybe it's a bad tank who doesn't know how to use his damage mitigation abilities. When that happens, if there's not a hunter who's had the presence of mind to turn Growl onto their pet, pick a dps'er and make them your temporary tank. Plate-wearer is best, but I've kept rogue tanks and mage tanks alive through bad pulls too. Pump your big single-target heals into them (they'll need them). If you have any cooldowns for them that will help them take less damage for a few seconds, use those, too.
When you get Rebirth, try not to forget to use it! I know I forget my druid's Rebirth a lot - I don't tend to play her much, and she's never made it to max level, so I'm just... not on-the-ball enough, as a druid healer, when I run a 5man ;)
It's *amazing*, the kind of pulls you can salvage from a wipe! Never give up in a bad situation. Just keep trying. And then just keep trying the next bad pull. And the next one. You'll be amazed when it all starts to click for you.