Originally Posted by A Laser Cat
I was poking each minion that was at full health while there was nothing else going on in the lane so that he could get to his last hits easier and quicker.
Well, that's the problem right there. Enemy minions spawn every 30 seconds. Whether you attack them down, or not, Graves is going to get the same amount of CS every 30 seconds. The only thing that matters is whether or not he can get the last hit.
A lot of AD Carries tend to think several steps ahead. In order to get each minion, they need to manage their health bars in such a way that no two minions are low on health at the same time--or else they might lose a CS. Because of this, when you the support accidentally or intentionally hit one, you can really mess up your teammate's chi.
To complicate things further, there's a time and place to push your wave, and a time and place not to. Basically, it's "ideal" to be as close to your turret as possible. But depending on whether or not your side has momentum (more minions) you either want to help push, or not. If your side already has momentum, then it's best to push your wave to the enemy tower, so that is "resets," and the enemy side gains momentum instead. But if the enemy side already is pushing towards your side, then you want to counterpush so that the enemy just barely has momentum, but is still technically inching closer to your tower without actually getting in range of it. This is called "freezing" the lane.
So yes, there is a time and place to use basic-attacks A.K.A auto-attacks. But it's always important to be mindful of your AD Carry's last hitting plan. And if they ask you to stop, then just go ahead and don't do it all. It's better to lose control of the lane then to piss off the teammate you're supposed to be supporting.
Support is my main, and what helps me a lot is when I try out ADC for myself. When I catch myself thinking things like "Man, I wish my support would help me last hit under my tower," then I know what to do the next time I'm the one playing support.