Attack range is far-and-away the most powerful stat in league, and ADCs have a leg up on just about everyone in that regard.
Furthermore: As a broad statement, ADCs are supposed to have weak and fragile early games in exchange for massive scaling and monstrous late game power. This varies a bit; Draven and Lucian actually hit their zenith in the mid game, then drop off. Caitlyn is hands-down one of the best laners (in any capacity) in the entire game, Ezreal can basically do whatever the fuck he wants and be strong at any point based on his build. However it is, by and large, true.
So with that in mind, it's pretty clear why ADC's need to be kept in check solo lane wise. Plenty of other champions, specifically the melee bruisers & fighters of top lane, sacrifice scaling and late-game potential in exchange for strong lanes and powerful mid games. This means that they're supposed to be strongest when ADCs are (as a general statement) at their weakest.
If ADCs become able to hold their own, reliably and effectively, against champions which are supposed to shit on them during their strongest phase.. They basically strangle everyone else out. Their damage is the wrong combination of safe and reliable, which when combined with their "only getting better with time & gold" design, means that the only thing which counters a solo lane adc is another, stronger, solo lane adc.