If you are around any ballpark long enough you will probably hear the phrase "two hands" mentioned at some point. I'm sure you can also remember seeing young players at youth camps getting their hands smashed with baseballs when trying to use "two hands" while catching fly balls. Outfielders are usually taught to catch fly balls using "two hands" but this is not the best way to teach the fundamental catch.
First of all, the catch is always made with one hand - the glove hand. Similar to the sweet spot on a hitter's bat, the glove also has a "sweet spot." The optimal area of the catch is where the index finger would position in the glove. Obviously we don't literally need "two hands" to catch the ball.
Many instructors teach two hands to catch fly balls because amateur players drop or miss fly balls. The real issue is youth players are not comfortable with their non-dominant hand and they need to learn proper glove positioning. Using two hands has two common flaws: 1) it restricts the ability to reach and 2) it creates a barrier to see the baseball.
Using the glove hand to secure the catch provides better reach and range of motion while providing a clear path to see the ball and make the catch. Once the catch is made, the transition to the throwing hand is quick and efficient as the player uses proper footwork to throw. Ideally, if the player has time to set up under the ball, the catch would be made as the glove-side foot plants into the ground.
Instead of "two hands while you're learning" we should focus more on one hand while we're learning! Enjoy the improved range of motion and unobstructed path to see the baseball into the glove.
Hope this helps.
See you on the diamond!