I'm being positive and assuming that the healer couldn't heal the tank due to the tank gear being inappropriate for the duty. Not that the healer didn't want to heal the tank because of their gear.

OP explained that another healer was able to heal them through the same dungeon with the same gear. OP, not all healers have the same skill. Some will be able to heal you, others won't. It's always best to ensure that you're well geared for the content you are doing.