Airplanes are generally designed so that if you stop messing with the controls they will level out. You can increase this tendency by doing things like set the wings higher and farther back, or do the opposite. However, the more stable you make the plane, the less responsive it is to controls. For a dogfighter, this responsiveness was very important, so fighter airplanes tended to be designed so that they were closer to the edge of stability. The Corsair pushed that limit which made it good for dogfighting, but terrible when you needed to make the rapid and precise adjustments necessary for carrier landings.
Modern aircraft usually have active computer assistance that allow the aircraft to physically be barely stable (or even unstable) with the computer interpreting the pilots inputs instead of the pilot directly controlling the aircraft. A flight sim will do this by default, or at least adjust the sensitivity of the input
An additional factor was that it was a single powerful prop engine. This created an asymmetry in flow that made the aircraft twist left at low speeds, or when the engine increased in throttle (such as when trying to land on a carrier, or trying to abort a failed carrier landing). This may or may not be simulated by a flight sim
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