Let me get this straight, you watched a video about a pro who knows what they are doing tell you what to do, and now you think you are a pro that knows what you are doing now? What you just did is the equivalent of someone calling themselves a doctor because they can google your symptons.
If you needed that video to tell you that, chances are you are one of those people that I didn't know how to handle, and thank you TheOddOne for showing people the way.
Let me blow your mind:
TheOddOne brought up a situation where you would not attack the ADC if you are the anti-carry, such as Jax. He said that there were 2 tanks in front of the ADC, in this situation Renekton and Elise. The distance between Vayne (their ADC) and their Renekton was 600. His argument for avoiding Vayne is that Vayne was not in position to do damage herself, thus would be pointless to attack, until she got in range in about 2 seconds.
Do you understand at all how movement speed functions in this game? Let me enlighten you. That magical number tells you how much range your character covers over a span of 2 seconds. FE: Master Yi's base movement speed is 355, so he covers a range of 355 over 2 seconds. Use this knowledge to your advantage.
That said, assuming Vayne has homeguard boots, lets say she has 400 movement speed (just pulled that number out of nowhere) with runes and masteries. That means you have 2.5 seconds to damage their frontline before Vayne gets to you, assuming you do not move forward. This means that you get 2.5 seconds of free damage on Renekton and Elise. After that period of 2.5 seconds, KILL THAT VAYNE. She is in range to do damage now. If you are Jax, your leap covers a range of 700, you taking Vayne out of the fight/causing her to focus you.
As soon as that Vayne is in fighting range, she has become the #1 priority. Bar none. No reason not to attack her if she is close enough to attack you if you are the anti-carry. By chasing here away or scaring away for lets say 2 seconds, you just prevented WELL OVER 1k damage late-game and possibly won they game by landing the kill.
EDIT: What my team is doing matters. This is a team game. If ONE GUY has no clue what he is doing, atleast 20% of your team is effectively useless and is not only hurting you, but helping the enemy team as well because chances are that ONE GUY will die due to his poor choice of focus. I have a friend who mains ADC and I've been coaching him through ranked play. When I first started helping him, he thought he should focus the ADC. I saw him lose a teamfight as Graves because he charged right passed an enemy Alistar to get to the enemy Ashe. He started attacking the Ashe, then died instantaneously because the Alistar knocked him up and he got killed. Afterwards, I told him to allow his Malphite, who was doing a great job, and Thresh, who was also doing great, to peel for him and explained to him what peeling is. After that, he overwhelming won his next time fight after getting a Quadra kill. Point is: Him knowing what he was doing changed the game from his team overwhelmingly losing fights to his team steamrolling the other team.