Okay, they are non-existent islands off the coasts of Spain and Ireland, respectively.
But the myths came from somewhere, right?
Hybrasil was on maps as late as 1865.
Antillia apparently is part of a medieval legend about events from the Moorish conquest of Iberia. By the High Middle Ages people were aware of various Atlantic islands and it made sense to them there would be a variety thereof scattered in the mid-Atlantic. One can imagine sailors and traders reporting that they had “sighted land” in the fog or bad weather, or fishermen describing legit islands around their fishing banks way out there, or the ocassional seafarer who may have unknowingly hit the Western Continent and made it back to tell the tale, or people looking up scrolls with older reports from antiquity, and in the telling and retelling the information about what is where and what’s it like becomes distorted and mixed up with other tales (e.g. St. Brendan’s).
Until very relatively recently, “uncharted islands” and their counterpart, islands that after being “discovered”, nobody else could find, were sort of expected things to encounter out at sea (see the Phantom Islands article in Wikipedia). We now know that there are small volcanic islands that emerge and are relatively quickly re-eroded down, or blow themselves up; and others that can be taken out by undersea landslide or subsidence; others are honest misidentifications and errors of navigation when describing the location.
According to Samuel Eliot Morison, Hy-Brasil means Isle of the Blessed in Gaelic. That does not agree with what Wikipedia says about the name, so perhaps it’s wrong.
At any rate, there does not seem to be any particular tale the island comes from, just general folklore. It’s an enchanted island, sort of a Irish Elysian Fields which moves around, so is spotted in a variety of places. Living people are not allowed on the island.
BTW, the name has nothing to do with the country of Brazil. You no doubt knew that, but not everyone does.
Some of it may be really well-preserved folk memory of drowned lands previously inhabited in the region. I doubt it, though, given the times involved.
But people also are perfectly capable of just making shit up.
And once someone has made some shit up, other people are quick to assume their idea had to come from somewhere. And repeat it.
Sort of apropos: xkcd: Citogenesis
It may also be the idea of “there just MUST be more land out there!”
For the Irish, “Hy Brasil” *equates *to the Isle of the Blessed. The Irish had a number of different names for their western phantom islands, all more or less describing the same place. I think Brasil comes from bras, "boastful"or bres “mighty” (with the latter slighly more likely, as the same phrase exists in medieval Welsh); Hy is just Í “island.”