Because it's kinda already happened, but not really? The thing about cheetahs is that they are very, very endangered, part of the reason being that cheetah cub mortality rate is something like 80%, which is abnormally high even for wild animals. Cheetahs don't make dens where they can stash their cubs, so they have to sort of drag them around with them and hope predators mistake them for a badger and don't attack them (cheetah cubs have very fluffy fur on top of them as camouflage).
Add in the fact that tjey're basically horse software running on cat hardware? These guys are an anxious wreck, every single one of them. And if left on their own they will absolutely form a positive feedback loop of scaring each other half to death and be too stressed to breed.
Enter wildlife conservation scientists.
These guys really want cheetahs to stay around, and stay wild animals. They are very fucking careful to let cheetahs be wild animals while making sure they don't perish entirely to enviroment, starvation and predation, and that they preferably breed.
Cheetahs see humans staying back and keeping a respectful distance but helping whenever they need it. Everyone who knows cats knows this is basically a marriage proposal done right.
So humans want cheetahs to be proper wild animals. Cheetahs have tried being wild animals and said 'Fuck that shit! That's hard! Come pet me and keep me safe!'
Add in the fact that cheetah gene pool is so fucking limited they can basically all be each other's organ donors, you also gotta bolster their diversity, preferably with healthy cheetahs from zoos, and those are so used to humans some of them will just come up to you and demand to be petted. If it's one of those that was raised with helper dogs? That's basically an oversized housecat, or at least it really wants you to think it is.
And there is also a historical precedent for this! Fucking pharaos kept cheetahs as pets, and if taken young they can be tamed in, like, a year. Tame cheetahs were noble gifts in the Ming dynasty. The Mughals used them as hunting animals (though it might have been carcals or leopards).
Quite frankly, the only reason cheetahs HADN'T been domesticated so far is because getting them to breed in captivity is real fucking hard, and consistent sucesses were achieved only in the seventies. The males need to have their bromance packs (pardon, coalitions) and females need to have a large area to roam. Kinda hard to arrange without a whole lot of land.
So this is, in fact, the exact reverse of bears.