Jonathan, the title character in the story, represents the individualistic human desiring to fulfill his personal search for perfection in the area that is important to him. For Jonathan, that field of endeavor was learning how to fly, in the ultimate sense of the act.
For most gulls, it is not flying that matters, but eating. For this gull, though, it was not eating that mattered, but flight. More than anything else, Jonathan Livingston Seagull loved to fly.
Being rejected as Outcast from the Flock was not a concern; the important thing was continuing the search for knowledge about the science and application of advanced flight, as shaped by the body of a seagull.
The Elder Gull, Chiang, serves as a metaphor for God, teaching Jonathan lessons that included the mechanics of flight but went beyond them to encompass the philosophical applications of the knowledge to serve his own purposes and to allow him to help others.
The trick, according to Chiang, was for Jonathan to stop seeing himself trapped inside a limited body...The trick was to know that his true nature lived, as perfect as an unwritten number, everywhere at once across space and time.
Fletcher Lynd Seagull becomes the first of Jonathan's pupils when Jonathan returns to the beach and the Flock. Fletcher has the same hunger to learn about flight as Jonathan did, but is angry about the rejection of the others. Jonathan's curiosity and desire to learn consumed all his energy; Fletcher needs to be forced to admit that his judgemental attitude harms only himself. The way for Fletcher to learn to fly starts with him learning to forgive.
Fletcher Lynd Seagull, do you want to fly so much that you will forgive the Flock, and learn, and go back to them one day and work to hep them know?"..."I do," he said softly.