It depends on your definition of carrying, bro. MId lane isn't the only way to carry, and many people (but not the majority) go there thinking it's about the KDA, not the objectives.
The adc melts towers. Their job early game is to farm up and fulfill their niche, either becoming burst AD casters mid-game to keep their hypercarry counterparts behind, or powerfarming to hit their powerspikes to the late-game. They can carry by taking towers, roaming, and taking every lane's tower if possible with the aid of minions, alongside inhibitors. They're also partially in charge of dragon control alongside the support and jungler. In teamfights, they deal sustained damage, and are generally the ideal role for focusing the tank (yes, I said that). Kills are always nice, but you need to be able to fulfill your role and gather a proper amount of cs no matter what your KDA is. Not dying is worth more than a kill.
The midlaner's job is usually keeping the squishies out of the game, particular teamfights and objectives. An apc uses their superiour range and/or cc to hit the enemy team safely with the tank protecting them at the frontline. They either fight from the backline, swinging spells, or use superiour mobility to maneuver around the enemy and destroy the adc whose sustained damage won't defeat burst in a perfect setting. In laning, they delay the enemy laner from snowballing, giving their team's squishies a chance at survival. Assassins are similar, so I won't go too far on that.
The support's job is dragon control, protecting the adc above all else, and aiding the team in whatever way possible. Micromanaging is important, as well as map awareness. Roaming is not uncalled for, and can aid the mid laner or jungler if need be.
Top laners are pretty diverse, so they fulfill whichever role is needed. Bruisers keep assassins in check, tanks are on the frontline and lock down the enemy tank while cc'ing the enemy team. Dps optional.
The jungler's role is various, and depends on the champion in question. Their job is not to win everyone's lane, but rather to aid them in winning the game. Stress is high, and decisions must be made. Do you go help top lane out, or do you drop a ward for them out of kindness and gank bot lane whenever you see the enemy jungler setting up his tent again? Do you want to trade that dragon for a free tower, or contest with a teamfight? Be it a tank, an assassin, or a bruiser, junglers fulfill different combat roles. But their objectives is mapwide, and they either help take towers, shut down particular carries, or snowball lanes. No jungler is going to be the same.
As you can see from here, every role is important and crucial to "carrying" the game. "Carrying" is less about singlehandedly winning the game for your team, but rather doing your part and contributing a significant amount to win the game. You're going to get dumb teammates, but that's the way it goes. The game isn't about killing the enemies, but how your team can work together and always achieve an objective.
And keep this in mind: jungling is less about mechanics, and more about strategy. You don't win the jungle by killing the enemies, you win the jungle by getting exactly what you want when you want by planning ahead. You need to control the jungle.
