I personally think the group you were with was mildly frustrated by you (whether you were not good enough, or took too long drinking, or afk'd, or something else) and the mage pointed out you weren't even trying by saying you weren't heal spec. As a result, the group decided they no longer wanted to carry you since you weren't putting in your best effort.
If you aren't the right spec while leveling, I personally feel like you're the equivalent to the guy who shows up with no gems and enchants wanting to raid whatever is current at the time. I honestly don't understand why anyone gets upset that there are consequences to not putting forth an honest effort.
I personally think that you may have little to no idea of what you are talking about.
You dont need to be heal specced to do those runs PERIOD. If you kick someone out of the group for drinking too much, you should quit this game. Please, I beg you. Do it for the children. Wouldn't that be amazing if dps had to spec differently for instances to put in their.. what was it? Best effort? Let me list some classes/specs that I have encountered oh-so-often while leveling:
Balance druid wearing feral gear.
Sub rogues without poisons.
Any rogue without poisons.
Mages not using any armor.
Warlocks not using pets.
Hunters not using pets.
Death knight tanks.
Dps paladins with RF up.
Tank paladins without RF up.
Best effort? Give me a break. If this guy was able to heal as a caster spec without a wipe that was a direct result of him not being heal specced, then he put in the adequate amount of effort (which is far above average in most cases) to complete the run. Dps like to be *#@!@@%s when they die and they always blame it on the healer. Don't be an enabler by making healers feel guilty for worthless stuff like this. His group was a bunch of clowns and that's what it should be left at.