You play a 1v5 champ such as xayah or kaisa, who can self peel whilst also dealing massive damage
And more importantly, it's not like there is any role that can carry whilst even, when your team is behind. It would be more unfair if an adc that goes even somehow manages to 1v5 the game, assuming that the enemy doesn't hard int and feed you.
Checklist:
Gold and XP Lead: Missing
Peel from Teammates: Missing (Yasuo and Teemo don't provide defense, unlike a tank or a malzahar or even veigar)
Scaling Advantage: Missing (It's a teemo that's behind, not a jax/tryndamere/kayle/nasus, and yasuo dying a lot early means that yasuo is bad and won't carry in the late game. More importantly, they have a Veigar)
Team Comp: Horrible for reasons above. Master Yi is useless without kills and cs, especially not when there is no frontline
As for 1v9 Ability -
Self Peel: Non-existent. You have your W and E, but that's not good enough. Things such as Xayah R, Vayne RQ, Ezreal E and Kaisa E + R are much stronger.
Steroid Ability: Non-existent. Unlike Xayah, Kaisa, Tristana and others, Cait doesn't have an on-demand damage boost. This is especially impactful when you don't even take Lethal Tempo, as it will result in a low DPS even with decent items provided that the enemies are fed. This doesn't mean that taking Lethal Tempo will solve your issues or even that it will have a positive effect given your playstyle, but what you need is good teammates
Early Game Oppression: Lower than Draven, nor did you create an advantage with your long attack range. Don't say that their jungler ganked so you lost, because obviously vision control and wave manipulation would have helped in that regard. Note that this is easier said than done, but is still a mandatory procedure to not getting destroyed. This also scales with the skill level and champion type of your support, as even Draven cannot win in a 1v2 against an Ignite Leona whilst having xp being stolen, if lux throws her abilities backwards.
You're not always going to have good teammates, but keep in mind that you also have your own bad games occasionally. And if it seems like your team always has more bad players than the enemy team, take into account the simple mathematics of your team having 4 people having a probability of x% of feeding/being afk/playing bad you get my point, whereas on the enemy team there are 5 people that have an x% chance to feed/afk, and so assuming that you don't become a liability to your team or at least not as often as the average player, and carry at a rate more frequent than the average player, you will find yourself gradually having a 55% or higher winrate.