Why is Belgian Dutch called Flemish when it is not a different language?

Because in this context, Flemish is a so-called pars pro toto. Linguistically spoken, not every Belgian Dutch speaker speaks Flemish. In Antwerp, for instance, people are talking a Brabantian variant of Dutch, not a Flemish one. Flemish variants you might hear in Ghent, and even more in Bruges. A third variant, Limburgish, is spoken in the east, near the Dutch border. Adjacent dialects are quite well mutually intelligible, while someone from Limburg will hardly understand a West-Fleming (unless they are talking Standard Dutch, of course).

In short, most Belgian Dutch speakers do not speak a Flemish dialect. But the term Flemish is used as a pars pro toto.

Belgium is divided in 10 provinces: I live in Vlaams-Brabant (Flemish-Brabant) which is, linguistically and historically spoken, a contradictio in terminis. Since Flemish serves as pars pro toto - to denote all Dutch speaking Belgians - the common meaning of Vlaams-Brabant is actually Dutch-speaking part of Brabant. The French speaking part of Brabant is called Brabant-Wallon (Walloon-Brabant).

The actual provinces of Brabant-Wallon, Vlaams-Brabant and Antwerpen form, together with the Dutch province Noord-Brabant the former Duchy of Brabant. And the Dutch dialects of the former Duchy are Brabantian, not Flemish.

The actual provinces of West-Vlaanderen and Oost-Vlaanderen form, together with the Dutch province Zeeland and with French-Flanders (Artois) the former County of Flanders, and its Dutch dialects are Flemish.

And both, Belgian-Limburg and Dutch-Limburg form together the former County of Loon, and its Dutch dialects are Limburgish.

Actually, same happens in the Netherlands. In many languages, Dutch is called Hollandic. My Spanish friends for instance, they are calling my native language olandès, although the official Spanish term is neerlandès. Same in France, where my language is often called hollandais instead of the official term néerlandais. This is a pars pro toto as well since Hollandic variants of Dutch are spoken only in the north-western parts of the Dutch speaking zone: the Randstad. In north-east they speak Saxon variants, in center south they speak Brabantian (as in Belgium), in south-east they speak Limburgian (as in Belgium as well) en in south-west they speak Zeeuws which is actually a Flemish variant.