Actually actually actually it is the exact opposite way around and more so the higher elo you get. The support plays to their ADC a bit but the way they play to their ADC is "I'm landing hooks on Soraka and Lucian isn't going in, maybe I should use my flay passive on her a couple times and then Death Leap and Flay her back so that she's closer to Lucian and has lower HP" not "My Lucian has been sitting here farming for the last 10 minutes and even though their Caitlyn is beating him in farm he doesn't seem to want to bully them so I'll sit here and play passive".
The support should fit the ADCs style
In order for a solo queue lane to work they both need to synergize at the same time the ADC should always be the one playing to their support.
Why?
Because the support is the one required to set up the plays and the ADC should never be the one to go in first provided normal 2v2 circumstances. The support is the one who should set up the play (unless you have a death wish for the ADC) because you don't want the guy who has all the damage to be taking the minion aggro. You want the one who has the utility to take the minion aggro as if they're the ones who die in the fight it's less detrimental than if the ADC dies. An ADC might poke without their support initiating but if the support never sets up plays, doesn't land good bindings, good hooks, good silences, good polys, slows, bubbles-- you shouldn't be getting any kills in lane.
So basically the ADC should look to their support in this regard. Is my support overly aggressive and charging in with her Zenith Blade every 6 seconds? I should pick up the kill or otherwise ping mia at river and tell her to wait for the enemies to push or for us to get better vision. Is my support a passive defensive support like Janna? If she hooks them with a tornado I should poke them a bit, otherwise I shouldn't think about going in.
It's the flash Tibbers, the Solar Flare, the well timed Dark Binding that wins you a trade and as such the support should do something of that sort to set up an engage for their ADC. the ADC should be the one playing to these engages and therefore the ADC's playing should fit the Support's style. The ADC only gets a real choice in champion select where if their support picks someone like Leona they can say 'Hey Leona I'm not really comfortable playing so aggressive can you pick a different support' and if they say no (or if it's teambuilder) your botlane is pretty much suboptimal anyway because you guys pretty much have two different views on the subject (and in teambuilder you just find a new support/team)
And I have no problem with them because I was SUPPORTING! her play style, which is what a support is supposed to do.
Not really. A support is supposed to control the flow of a teamfight with their CC, Peel, and Utility (including Ally Sustain and Buffs). A support can 100% ditch their ADC after laning if they feel like they won't get anything out of helping them. If I have a 5/0 Ahri and a 1/1 Jinx who blantenly missed her last hits I'm focusing on keeping Ahri alive and then if I have peel/heals leftover I'll turn on who jumps on you and flank them. It's only my job to protect that ADCarry because they're the ones who are doing all the damage, if you're not doing the DPS I don't need to play to your style at all because I am THE TEAM's support NOT the ADC's support.
So I think I should get to choose how aggressive or not aggressive my support is if I'm ADC.
Naw a lot of supports can only play to a certain level of passivity or aggression because of their kits (a Leona with a passive ADC is pretty useless and Soraka with an overly aggressive ADC who lacks the damage to 1v2 is also pretty useless). If you're support-- playing the role of basically the ADC's guardian or mother for 20 minutes, and you give up your authority as mother it doesn't mean that other parental figures should give up their maternal authorities because you think a good parent lets the kid be in charge. That's what a start game ADC is, a little kid. They're item dependent, champions who need to be fed gold to grow into a monster. You play to that specific carry's power spikes in terms of aggression (Corki has a pretty strong level 2 whereas Cait doesn't really gain as much from her Level 2, therefore if you were Leona with a Corki you would for sure want to go in level 2 for the kill but if you were with the Cait you might start E or try to melee Q from a bush or wait until you get your shield level 3 and Cait has poked them down before you go in) but your ADC doesn't get to look at you playing Blitzcrank and say 'I like my Supports to play passive, kay?'