The exact timetable of cat domestication is a little difficult to establish due to the similarities in skeletal structure between (recently) domesticated and wild cats. For the most part, scientists believe cats were domesticated through a commensal relationship, which is a relationship that benefits one species while have a negligible or positive impact on the other (1). This is supported by the fact that it took several millennia for there to be unquestionable differences in the sizes of domestic and wild cats (Egyptians probably lived with cats as early as 10,000 years ago, but clear differences don’t occur in wild and domestic cats until 5,000 years ago in the Uruk period) (2). Commensalism often turns into domestication more slowly, as the wild animals are beneficial to humans without significant interference. This commensal relationship means that no one set out to domesticate cats unlike, say, cows or sheep, which were specifically bred for a purpose.

There never was any specific decision to domesticate cats (or let them domesticate themselves), but people probably started feeding them and encouraging them to stick around as a form of pest control (6). As cats began to hang around more, they were most likely taken in as pets, as pet-keeping is incredibly widespread across many different societies, so their domestication was at least in part driven by people developing a bond with cats (8).

Cats were most likely first domesticated in Ancient Egypt. The evidence for this includes the fact that all modern domestic cats evolved from the North African subspecies Felis silvestris lybica, the presence of Egyptian paintings of cats from 20th-19th century BC, and the spread of cats from there to Cyprus (which had no native cats), which indicates a conscientious effort by traders to bring cats with them. However, a recent study by Yaowu Hu, et al. has also argued that cats were domesticated separately in China, in similar ways that they were domesticated in the Near East. This argument is based on isotopic data that showed that cats were eating a significant amount of millet-based foods, which suggests they were getting fed and the presence of a skeleton of an older cat, who may have been kept as a pet due to its age (3). However, others have pointed out that the data is more ambiguous than Hu makes it out to be, and this domestication would still have occurred after the appearance of cats on Cyprus (4 & 2). Additionally, the Chinese cats were members of Prionailurus bengalensis, so if these cats were ever truly domesticated, they did not remain so, as modern domesticated cats in Asia also descend from Felis silvestris lybica (2). These domesticated cats did not reach China until after 200 BCE (8).

However, in both the Near East and China, cats were domesticated from a previously commensal relationship, and both occurred in agricultural areas, showing that cats were domesticated because of their ability to control rodent populations and protect grain yields. That cats were taken to Cyprus shows their utility in keeping rodent populations under control both on land and on the sea.

The relationship between people and cats also varied across history. Greeks and Romans tended to keep cats as curiosities and relied on ferrets and polecats for dealing with rodents. The Romans were also most likely the ones who brought cats to northern Europe. During the Middle Ages, cats became demonized by the Church due to their association with pagan cults and unorthodox beliefs. In the later middle ages and early-modern period, cats were associated with witches. The negative association of cats and women is not exclusive to Europe either; malevolent cats were also present in Japanese myth and folklore, often associated with promiscuous women (8).

However, by the sixteenth century, exotic cats (and dogs) had become “an expression of status and identity” as well as a source of joy in Europe. Exotic animals were used as expensive gifts among European elite, but they were also admired for their beauty. Isabella d’Este of Mantua owned one such cat, although it unclear whether it was a tamed wild cat or a domesticated cat. In either case, the cat was valuable due to its unusual looks and size, indicating that cats were prized not just for their ability as rodent catchers but as companions and pretty pets as well (9).

It is also important to keep in mind that there debate on what exactly ‘domestication’ means. It has variously been described as (a) “a mutualistic, symbiotic relationship that benefits both domesticator and domesticate,” or (b) genetic changes in the domesticate phenotype, or (c) the relationship between people and the domesticate (5), or (d) when humans take control of an animal’s breeding. Under the first four definitions, cat domestication was complete 10-5,000 years ago, but if using definition (d), cats weren’t fully domesticated until 150 years ago. When humans did begin breeding cats, it was more for aesthetic purposes than for specific traits (f ex. Dogs are also bred for hunting, herding, etc)(7). In fact, "22/38 of modern recognized breeds were only registered in the last 100 years." Older breeds were the result of geographic isolation, while modern breeds are the result of deliberate human intervention (8).

So, yes, cats do serve a functional purpose, but they were also kept simply because people thought they were cute and made good pets. The relationship has also not remained static throughout history.

(1) Driscoll, Menotti-Raymond, et al., “The Near Eastern Origin of Cat Domestication,” in Science Vol. 317 (2007), 519.

(2) Vigne, et al., “Earliest “Domestic” Cats in China Identified as Leopard Cat (Prionailurus bengalensis)”, in PLOS One (2016), https://doi.org/10.1371/journal.pone.0147295.

(3) Hu, Wang, et al., “Earliest evidence for commensal processes of cat domestication”, Proceedings of the National Academy of Sciences in the United States of America (2014), http://www.pnas.org/content/111/1/116.

(4) Bar-Oz, Weissbrod, Tsahar, “Cats in recent Chinese study on cat domestication are commensal, not domesticated,” in Proceedings of the National Academy of Sciences in the United States of America(2014) , http://www.pnas.org/content/111/10/E876.

(5) Melinda A. Zeder, “Core questions in domestication research”, Proceedings of the National Academy of Sciences in the United States of America (2015), http://www.pnas.org/content/112/11/3191.

(6) Claire Hargrave, “Cats and domestication—a road less travelled” Veterinary Nursing Journal 30:9 (2015), 263.

(7) Erin McKenna, Pets, People, and Pragmatism (2013, Fordham University Press), 185.

(8) James A. Serpell, “Domestication and History of the Cat,” in The Domestic Cat: The Biology and Its Behavior, eds. Dennis C. Turner and Patrick G. Bates (Cambridge University Press, 2000).

(9) Sarah Cockran, “Sleeve Cat and lap dog: Affection, aesthetics, proximity to companion animals in Renaissance Mantua,” in Interspecies Interactions, eds. Sarah Cockram, Andrew Wells (2017, Routledge), 34-65.

Would this question be better suited for /r/askanthropology?