How come only nine “Free Cities”? Lots of other Valyrian settlements are shown on the maps, like Selhorys, Mantarys, etc. Why aren’t they considered Free Cities?

WOIAF explains this explicitly: 

“We speak of Nine Free Cities, though across the width of Essos one may find many other Valyrian towns, settlements, and outposts, some larger and more populous than Gulltown, White Harbor, or even Lannisport. The distinction that sets the Nine apart is not their size but their origins. At their height before the Doom, other cities, such as Mantarys, Volon Therys, Oros, Tyria, Draconys, Elyria, Mhysa Faer, Rhyos, and Aquos Dhaen were grand and glorious and rich, yet for all their pride and power, none ever ruled itself. They were governed by men and women sent out from Valyria to govern in the name of the Freehold.”

“Such was never true of Volantis and the rest of the Nine. Though born of Valyria, each was independent of its mother from birth. All but Braavos were dutiful daughters, neither making war upon Valyria nor defying the dragon lords in any matter of significance; they remained willing allies and trading partners of their mother and looked to the Lands of the Long Summer for leadership in times of crisis. In lesser matters, however, the Nine Free Cities went their own ways, under the rule of their own priests and princes and archons and triarchs.”