For a long span of history, in many parts of the world, peasants lived largely in an autarkic economy. They'd produce their own food and clothing, not needing much beyond that. Trade existed in kind or with a limited monetary component. The pressure to produce a surplus much farther beyond their needs often came from State coercion obliging them to pay taxes in some shape or form.

Especially the further back you go, the head of the family would divide up family members to do different tasks, from tilling the fields to making textiles to herding domesticated animals. Purchasing textiles was unnecessary since what little was needed could be made on the spot. Because there was no dependable, large, locally accessible market, trade specialization, such as tailors, made little sense.

The neolithic revolution (when farming became the basis of society, as opposed to hunting and gathering) led first to villages, but it took centuries or (in some cases) millennia for those villages to become tightly packed cities. Once cities did come about, you began to see labor specialization. Merchants, tailors, those making wine or beer, etc. Keep in mind that even though these specialized workers did come into existence, it was often a slow transition and even urban workers often had rural plots where they produced much of what they needed.

In this way, knowledge of textiles came about before specialization and professionalization of textile production became a reality. As the surplus grew, so did the ability for a society to have labor specialization, and thus markets for goods. As markets grew, it made more sense to travel between cities selling goods. This created trade networks. As trade networks grew, you saw even more specialization.

For example, M.I. Finley wrote about it in The World of Odysseus. The women of Greece's 'Heroic Age', as depicted in the Odyssey, would produce textiles for home use and make it to their ultimate wearer's size. Most people didn't go out and buy textiles themselves. Those who might buy textiles, especially luxury textiles, were part of a leisure class which had the wealth to do so and responds to a far later date from the inception of textile production.

In the case of the Caribbean at the time of Columbus' arrival, the peoples we call Taíno would produce their own cotton based cloths, fit them, and wear them, all without need of professional tailors.

Bibliography:

Levi Marrero: Cuba: Economia y Sociedad, Vol. 1

Lewis Mumford: The City in History

Sven Beckert: Empire of Cotton: A Global History

M.I. Finley: The World of Odysseus