Planet of the Apes is set in a post apocalyptic society that is controlled by apes. The people living in this society are treated as animals as they are hunted down and experimented on. In the beginning of the movie, you see how humans are being treated and how essentially they are nothing more but wild animals. They have no actual thought processes, have no recollection of their language, and are just there to serve the majority population.
There are a lot of instances where I thought the probe being addressed was more relate to how the people were being treated. However, throughout the movie you begin to see the societal hierarchy that the apes have in place, which is probably what ultimately led to the downfall of society the first time around. Dr. Zaius is a prime example of how people of higher statuses typically abuse their power in society in order to keep the people under them in line. Dr. Zaius as the lead ape and villain, constantly puts down Zira in her discoveries and thoughts of a possible society before them. Though he is fully aware of the truth, he does this because this idea alone goes against their religion and everything he has made this society believe.
In doing this, violence, marginalization and the idea of powerlessness is used in order to gain full control of this society towards humans and other apes as well. The gorillas use violence in order to incite fear into the people, while the orangutans are using force and abusing their power in order to have control over the chimpanzees. By doing this, knowledge is limited within the society which allows further control over them. Besides how the people were treated, I feel like big part of this movie was showing the power of government control and how much it can affect society. Even with the potential problem this may have case in the previous society, the one thing the apes held on to was government control and societal hierarchy. There will always be some sort of greed for power within society.