This parable is shown to be a kind of allegory for the quick passing of time and how swiftly we move from childhood to old age. The school that the boy at the beginning of the story goes to stands for the lessons that humans learn in the school of life. Note how the school is refered to and in particular the kind of lessons that are learnt there:
As our path revealed itself to us, however, we did not find it as totally sweet and unclouded as we had presumed. Dust-laden winds and unexpected accidents came about suddenly, so we had to be watchful, at the ready, and very patient. It was not all a matter of playing and fooling around. Rivalries could bring about pain and hatred or give rise to fighting. And while the lady would sometimes smile, she would often scowl and scold. Even more frequently she would resort to physical punishment.
References to the "path" clearly indicate that this school is more than just a school where students learn how to read and write. The pupils at this school learn about the vicissitudes of life and the need for patience and constant alertness. They learn too about the way that friendships cannot be depended upon and the pain that comes through betrayal. Lastly, they learn about the way that appearances and reality do not always match, and how deceiving some appearances can be. The ending, and the reference to the sudden realisation of both the speaker and the reader that he is now a grandfather indicates that the parable is a reference to life and how quickly humans pass through it, learning constantly.