How do I carry as ADC? I genuinely have no idea what I'm supposed to do when my team is focused on constantly diving the other team's back line and leaving me totally helpless. It doesn't matter how many kills or CS I get when it's me against their front line every fight. I can only position and kite so much.
Shoot everything in front of you. There's a misconception about avoiding the tank and going straight for the carries, but sometimes you have to kill the tanks first. It's really dependent on your team composition.
Like just to throw an example out there. Jinx melts front line very fast. So lets say you're graves and their adc is jinx. If at same or similar items there's just no way you're gonna kill their tanks before she kills yours. So it make sense for your team to dive her and then your job is just to stay alive longer than her so they can peel back for you (if other team is smart they will be peeling for her instead of diving for you).
However let say your team is composed of two tanks, control/utility mage mid (think Ori/Lulu) and you + mage support. Other team is pretty much the same thing. In this situation it's more of race of which team can kill the other tank first rather then diving the back line. In this scenario both teams should be peeling for their respective ADC.
My only advice when fighting their front line is flash early. Don't ever get hit by their cc or you're pretty much done. You're most likely all offensive items or all but one (late game). So you just have to find a way to dps constantly non stop, and if you put yourself into a bad situation where you get cc you're either dead or you're running for your life and not dpsing while the other adc is. Either way you're losing the fight if you're not dpsing.
Here's two video example (I picked both with Graves just so you can kind of get a sense).
Example #1
https://www.youtube.com/watch?v=_Yaaa1rsTP0#t=63m50s
There was just no way Graves was going to kill Maokai/J4 faster than Ezreal/Corki kill Fizz/Reksai. So Graves took a risk.. and it worked out.
Example #2
https://www.youtube.com/watch?v=OlGdSz4tzcE#t=48m20s
This time you notice Graves spent the entire fight, fighting the two front line Irelia/Reksai. He never went for their carries but focus tank first and stayed the hell away from LB who can 1 shot him, and Annie who can stun him which leads to death.
So same champion but in one scenario took the risk went for back line, other peeled back and kill tanks. You'll get used to what to do for in certain situations over time.