History.
Much like the Dark-typing of years' past, the Fairy-type was long suspected to exist, but was denied any official recognition due to associated superstitions.
The current leading theory is that Pokemon typings and powers come from these creatures harnessing a sort of supernatural power present in each element. For example, Water-type Pokemon would harness this power, as it appeared in water, the liquid. Infamously, researchers at the time did not want to recognize the Dark-type for fear of what it would mean if power could be drawn from sources of darkness. Similarly, they did not want to acknowledge the fae's existence, and so refused to look into the Fairy-typing.
Despite this refusal by scientists to look more into the unknown energy being harnessed by many Pokemon of the time, some individual Trainers took it upon themselves to research, recognize, and even specialize in the Fairy-type. Ms Opal of Ballonlea was one of many who did this, as she trained and specialized in Fairy-types for many years, before it became recognized only relatively recently. (This is why she was known as a "mixed-type specialist" for many years.)
Fairy-type's existence, though, was still unknown on a large scale, until Pokemon Trainers with then-unrecognized Fairy-types began to come together on forums, discussing their Pokemon's odd abilities which were not explained by the current framework of 17 typings. What was initially one instance of this niche type of board, titled "Unexplained Pokemon Powers", established in 2005, eventually grew in size, until there were thousands of visits a day from Trainers who had heard that they were not the only ones who had Pokemon like this. This sudden increase of public awareness of a possible 18th type forced the hand of researchers, and they were pushed into looking further into the possibility of the Fairy-type (as it was then the most-plausible lead that they had for an 18th type). In the next few years, multiple studies were published which supported the existence of the Fairy-type, until, finally, in 2013, the Fairy-type was recognized as a Pokemon type
Of course, researchers of the time were quick to reassure everyone that 'Fairy' was 'just a word', and that it hardly meant that tales of the fae held any water. However, many find it notable that the majority of Fairy-type specialists do, in fact, believe in the fae.