As indicated by the comment, from my answer to Animation: floating island, flying pests, this might be Skywhales from 1983.
The story begins with a man warning the tribe of approaching skywhales. The drummers then warn everybody of the hunt as everyone get prepared to set "sail". Except one man is found in his home sleeping as the noise wake him up. He then gets ready and is about to take his weapon as he hesitates then decides to go. As he leaves his room, his wife and child see him and try stopping him. He goes through the forest with strange fauna and flora and stops at a path as he sees old pale natives head into a strange silver building. As a sign of respect, he shields his eyes as a sign of advanced culture. He is then surprised when his wife pokes him and says that she's coming. As he enters the ship, he sees a native wearing the captain's hat but then he takes his rightful hat while the other looks surprised he came. Then they go on a hunt for the whale where at this point the audience is now aware they live on a floating island high up in a gas giant. They go far away from their home and stop when they hear the whale. Everything is still until a skywhale comes and then destroys one of their ships(the one that has the main character). They parachute down to another ship (the one where the wife is steering) and follow one of the two whales (because one escaped). The main character then harpoons its head (explained above) and is congratulated by his team as they fall down because the whale has 2 harpoons in its head. As it dies they bring it back to their island home where it is completely butchered by nightfall. It then shows the main character and his family at the port where Mom is talking to the son and the main character is tying a rope. Suddenly he turns pale and his eyes black. The Mom immediately recognizes what he has become and adopts the custom of shielding her eyes and his son soon follows. By instinct, the main character heads to the building where all those who reach the point in their life to mature go. In the building, there are four guards and a giant hole in the center. Skywhale drawings are all over the floor. As the guards cover their eyes and the mom and son watch at the doorway, he stands there for a while and then falls in the hole. The son gasps and tries to enter but the mom stops him. He looks confused and as they leave, he asks something to his Mom which then begins to explain something to him. They then show the main character falling through the roots of the island as a cocoon starts forming around his body. By sunrise he is completely enclosed and hatches as a juvenile skywhale. The viewer then sees the mother with the main character's spear explaining something to the son. Suddenly he hears a skywhale's call, takes the spear, and points it to the whale which he immediately recognizes is his dad. The two of them then stand there staring at their dad/husband fly away into the sunrise with the son saluting him with his father's spear. At this point the end credits appear with primitive skywhale cave-drawings in the background.
Found by searching for cartoon creature falls through center of island and becomes winged