Since cast iron pans have rough and porous surfaces, when you cook eggs in them, the proteins in the eggs react with the iron and make them adhere to the pan's surface. From there, tiny bits of the eggs settle into the minuscule crevices in the pan’s surface, producing a sticky, unevenly cooked mess and leaving stubborn residue behind.
While a seasoned cast iron pan is somewhat non-stick, its heat-retaining properties increase the risk of over-browning and overcooking your eggs, making it difficult to stir and flip the omelettes. Greasing the pan doesn’t help either, as, according to "Fresh Eggs Daily Cookbook" author Lisa Steele, eggs often stick to iron regardless of how much fat you use.
In an interview with HuffPost, Steele advocates for "a good steel pan or an enameled skillet" instead and highlights that it should be "a very shallow pan with sloped sides," which will make flipping and folding the omelette a much smoother process. Look for a nonstick option that's also thin and lightweight, so it heats up quickly and is easy to handle.