OP, most people talking about carrying are specifically talking about ADC, and how difficult it is to play vs junglers/supports since early S4. They have such a big power spike/increased gold income, even if you get a few kills you can't really compete with a sated shyvana with randis, or a triforce/frozen heart udyr, or a support with a full tank item/sightstone/face of the mountain regardless of how badly he did in lane.

ADC's went from a very carry based playstyle, to more of a spam sivir, farm for the entire game, and hit R in team fights. Some specific adc's with high kiting potential can dish out damage in the current meta(i.e. kalista, vayne) and those are the only things close to what it felt like to be a carry in S3.

It's not that it's good for supports either. Relatively speaking, supports were much better off in S3 when they had infinite wards, oracles, no trinkets, pink wards that weren't visible, and adc's who were strong enough to carry the game. There's a reason Challenger has almost no supports these days even though they got "buffed." Their role has been split up to all 5 members of a team, and on top of that winning lane means far less since ADC's have less impact on a game. Support now is like a lower income tanky top laner who has a bit of control of your marksmen laning phase. Before you were a vision controlling monster who had almost full say in how well your lane would go, and every play you made would add up to an advantage. In S3 you'd know if you had even 1 ward over someone after backing, enough to buy a pink and deny bush control for example. The game was much easier for supports to show talent on. Now, everyone has a free sightstone first back, and it's harder to mess up or outplay anymore.