Would you ask, “Why should humans be saved?’. You wouldn’t. It’s only humans who ask these questions because we have the power over animals to decide if they should or should not be saved from extinction in the wild. And that is what the question is asking. Even if the cheetah becomes extinct in the wild there would be captive, inbred cheetahs for many years until the captive ones died out because they were all sterile.
It is an impossible question to answer really because you can ask it of any animal. And I don’t think we have the right to decide what animals should be saved. They all have equal rights in a civilised world (which this sadly is not). On ethical grounds I don not believe that we should ask the question. It is also a question of failure and doom. Humankind should not be at in a situation where we have to decide to save the cheetah from extinction. We should take action well before that moment.
But if can put aside the equal rights argument and the sad fact that humans can play God then the reason why cheetahs should be saved is because their presence on the planet enhances it. They make the planet a better place.
They are beautiful and graceful, the fastest land animal and an important part of the planet’s biodiversity. They are an important animal. We are used to having them around. We enjoy watching them in real life on the plains of the Serengeti, in videos and on wildlife documentaries.
Also throughout history the cheetah has demonstrated a distinct propensity towards domestication. Of all the wild cats except for the snow leopard, they have a personality most suited to domestication. There are many examples of friendships between humans and cheetahs. They are a retiring, shy large cat species. And there many examples of hunting with cheetahs. I don’t like the latter but it reinforces the connection that humans have with the cheetah. It is a special relationship. I can think of no other large wild cat that has been as close to humans as this beautiful cat.
It is also unwise to let one species in a biome become extinct as it affects many other animals who are connected to it. There would be a knock on effect. To let it happen and not save the cheetah would be a clear sign of human failure to care for the planet. We are charged with that duty whether we like it or not and whether it makes us feel like gods or not. To let the cheetah die out would be an abdication of our solemn duty to protect the planet. It would take from our children and their children the joy of living in harmony with the cheetah which should be our immediate and long term objective. Our children for eons to come would blame us for this failure. Do you want that legacy?