IAAPilot (Fixed-wing back in the 80s and rotary-wing in the 90s). You asked about airplanes, but let me say this about helicopters: You cannot fly one without training. Helicopters are inherently unstable.
On the other hand, airplanes are usually inherently stable. That is, if you deflect the controls and then let go of them, the airplane will return to stable flight. For example, if you push the nose down, dive, then release the controls, the airplane will pitch up due to the increase speed and lift. When it pitches up it will climb higher than the starting altitude and slow down. It will pitch down and speed up again, but to a smaller amplitude than the initial dive. When the speed picks up it will climb again, but it will not climb as high as the previous time. The oscillations will become smaller and smaller until the aircraft returns to its original altitude. (Of course you have to take into account local weather conditions, fuel burn, etc.; but it’s close enough).
Have you ever flown a balsa-and-tissue airplane? You wind up the elastic band and put it on the ground and let it go. It will take off, climb, fly in a circle and land (if you built it right). Given enough space and a perfectly trimmed airplane, and a little nonchalance about where you land, an airplane should fly itself. Okay, we don’t all live on a huge lakebed. What about flying a real airplane?
Taking off isn’t that difficult. Just keep it lined up on the runway. Okay, there’s more… You have the P-factor to deal with. This is caused by the propwash that spirals around the fuselage. It causes the airplane to bank, so you need to add opposite rudder. You also need to watch your airspeed. Too slow and you stop flying. This is called a “stall”. Easy enough to recover from if you have the altitude, but it can be fatal if you run into the ground before your wings develop enough lift for flight. And you don’t want to hold the airplane on the ground when it’s going fast enough to fly. Wouldn’t want to get into pilot-induced oscillations and start banging stuff on the ground. But as long as you don’t stall, it’s easy enough.
So you’ve managed to take off without killing yourself. As long as you don’t get too slow and stall, you’ll probably be able to control the direction and altitude of the airplane. Piece of cake. A child could do it. Many, in fact, do.
And now the landing. While all flying can be said to be an exercise in energy management, this is where you really get the practical application of energy management. The game is to run out of flying speed at the same time that your wheels hit the runway. Oh, and it would be good to actually be on the runway and heading lengthwise, into the wind. You need to line up with the runway, heading upwind. Then you have to get down. Don’t dive. The elevators are really there to control your speed. It’s thrust that controls your altitude. Throttle back to get down. Don’t get to slow and stall close to the ground. Keep heading toward the runway. Be ready to advance the throttle in case you’re going to be short. If you’re high, you need to do something so you don’t land long. Flaps, a slip, or just throttle back and descend more rapidly if you have the room. Energy management. Landing is the hardest part, but it’s also often the most satsfying. Non-pilots have been “talked down” when the pilot became incapacitated.
Is it hard to fly? Not really. It just takes training and practice.