Central America is a subcontinent. Well, why not?
Speaking as someone with a degree in geology — there is a fundamental difference between continental crust and oceanic crust. Australia has the former, and the Pacific Islands have the latter. Australia may constitute a continent in itself, but “Oceania,” never. (Did anyone else get confused reading about “Oceania” in Nineteen Eighty-Four by George Orwell?) The basaltic rock of the Pacific Islands, instead of the mafic rock of the continents, is why Fiji water tastes so different from Evian.
Europe and Asia being separate continents just makes no sense at all, geologically. As Malcolm X noted, if you just look at a world map it’s obvious that Europe is nothing but a peninsula of Asia. Counting it as separate has nothing to do with geological facts and everything to do with Eurocentric cultural assumptions (blame it on ancient Greek racism and ignorance of world geography). I propose that Europe is a subcontinent of Asia.
If you say North America and South America are one continent because they’re joined by a little isthmus, then you must also think Chang and Eng, the Siamese Twins, were one person. Anyway, in geologic history NA & SA used to be disconnected (in the Cretaceous — breakup of Pangaea) and only very recently (in geologic time: the Miocene), thanks to continental drift, were they accidentally joined up.