When playing or AD carry you are likely the main target of the enemy team. You have the most potential to do significant and consistent damage and clean up after a fight, and chances are you’re the easiest person to kill on your entire team. AD carry often takes the most finesse to play and your mechanical skills are put to the test in each and every game.
Whatever League or division you are in I bet you’ve heard someone on your team flame you to stop focusing tanks in teamfights. Heck I’ve had it happen in Platinum on multiple occasions and I can only imagine how much worse it is in Silver or Bronze. Sometimes (rarely) in higher Gold divisions a team will peel players off their AD carries but if your rating is anywhere below it’s likely your team consists of headless chickens who chase whoever the heck they like rather than help you survive.
As an AD carry there’s only one way to deal with it, and it’s definitely not the worst of options: focus the tanks. The exact thing you were told not to do dozens or even hundreds of times is exactly what you should be doing in teamfights, as a dead AD carry is dealing no damage to anyone. Obviously if you have options then by all means go for priority targets, but when that Skarner or Lee Sin dives the backline and tries to kill you don’t be afraid to hit him. The worst option is to keep running away from them endlessly without even doing damage: make sure to kite them and autoattack as much as possible, typically when they drop below half HP they will either turn back and/or your team will switch their focus on them.
In fact as far as the rest of your team goes in a significant number of matches it’s very much possible that the annoying tanky champion could easily be bursted down to low health before he even gets close to you if only everyone actually bothered to do any damage to them. If everyone on your team just used one or two spells and a few autoattacks on the Skarner who tries to initiate a fight chances are he’d think twice about doing it with low health, and even if he did he would be fairly useless in that fight. Save your gap-closers or ultimates for a better opportunity on other targets, but try to use low cooldown spells and attacks on others.
An AD carry needs great mechanical skills and even better positioning to be successful, so the point is that you should never dive their back line in order to finish someone off unless you know you can 100% get away with it. Just remember what I said: if you’re dead you aren’t damaging anyone.
For everyone else who doesn’t play AD carries often and doesn’t understand their mechanics, help your carries! Helping them get away from tanks and bruisers can be even more effective in the end than going for the enemy carries. Do not whine about your carry focusing tanks when he clearly has no choice, instead think about why he’s focusing them and see what you can do to help it. I guarantee he wants to kill more important targets just as much as you do, but not at the cost of his own life.
Bottom line is you need to help your carries. It’s called peeling, and works well in Bronze or Challenger level. Lower-rated AD carry players don’t have the positioning, knowledge or mechanics to fend for themselves and you should always make sure nobody gets close to them. In a lot of cases you’re the one who should be focusing whatever your AD carry is focusing, not the other way around. Even if the target is a tank.