The thing with Sonic the Hedgehog 3’s Carnival Night Zone barrel is that a lot of people on the internet like to exaggerate how difficult it is to figure out and traverse. I understand why. It creates a nice sort of "myth" and gives people another reason to dump on the series. People enjoy the "actually, Sonic was never good, actually" line.
My own feelings about the barrel are complex. What is the barrel? What does it stand for? And why?
Those aren't really questions I'm equipped to answer. But I can absolutely chastise you all for ever struggling with the thing.
First, it's incredibly simple to get past. Sonic the Hedgehog 3 is a game that uses the D-pad and one button - when your one button doesn't work, you'd think you'd try the only other thing on the controller. When it's going up and down, nobody tried pressing "up" and "down" on the D-pad? The effect is instantly noticeable. I managed it at the age of six, and I was a cataclysmically stupid child. Also - crucially - there are triangles (or "arrows") pointing up and down, printed right there on the barrel. They match the up and down symbols on the Mega Drive D-pad. All the clues are there. They always were.
Second - and directly contradictory - I have no problem with games having one or two "what the hell do I do now" sequences or gimmicks in them, because they always end up being interesting and memorable. I don't see why in a game with an otherwise consistent difficulty curve like Sonic the Hedgehog 3, they can't throw something like that in at the halfway point as a "puzzle" of sorts. Not that it is actually a puzzle, as a barnyard animal (for example a cow, or a rooster) could figure it out. But I digress. For the purposes of the brilliant point I'm making, it will be considered a puzzle.
Now, comical hubris aside, people clearly did get legitimately stuck on the thing, which is why it came up in the first place and erroneously entered the annals of Bad Game Design History. It will never cease to amaze me how it's recalled with the same hostility as the car keys puzzle in Phantasmagoria: A Puzzle of Flesh, the goat puzzle in Broken Sword or the moustache puzzle in Gabriel Knight 3. Those are all fundamentally problematic examples of puzzle design. The barrel isn't. Let's stop pretending otherwise.