What is a apes life cycle?
Apes are primates, and primates go through an ovarian cycle, meaning that to some extent, all primates have 'periods'. Since humans are apes, of course they can have a period!! Other non-human apes (gibbons, siamang, orangutans, gorillas, chimpanzees and bonobos) also go through this cycle, although it is less pronounced. They do still menstruate however.
Chimpanzees have basically the same life cycle as other great apes (bonobos,humans,gorillas,orangutans) They are infancy,childhood,adolescence, afulthood, and old age. Of course, the length of these differs depending on the species of ape, but they are roughly the same as in humans, just slightly more accelerated.
The lesson is that there is a curse which goes with being the highest form of life on a planet. It is an arrogance which says that no other life can possibly be higher. The human astronaut knows this belief is false, and so does the audience, but the apes will not believe it. The arrogance of the apes is a metaphor for human arrogance.