Mostly because an ADC can heal-bait, while a support can't really.
If you think you can burst kill me, but I have heal as an ADC so you can't, then I have enough sustained damage (and late game lifesteal) to get the kill on you. I may not have the reflexes to exhaust you before enough damage has come out that it barely matters.
If you think you can kill a support and he heals, what's he going to do? Hit you with a wet spaghetti noodle a few times before it wears off and you kill him anyways? :P
Also, as an ADC I'll often be focused early in a fight. I may receive peel at some point, but since I was focused I took damage early. So if an ally is almost dead in a teamfight I can heal and we'll both benefit. Often supports are ignored in the early stages of a teamfight, so if they heal for an ally they'll waste the self benefit.