Why do many people believe Columbus discovered North America?

During the Renaissance period in Europe, ca. 1350-1550, there was dramatic development in a multitude of areas. Exploration was among them. Although historians may have, for a time, overstated how stagnant and isolated Europe was during Medieval times, nonetheless the continent was coming out of a sort of slumber. For this reason, European accomplishments seemed new and unprecedented, even when they were not in broader historical terms. Europeans saw these accomplishments as epic and their significance became exaggerated, owing also in part to the Europeans's (and specifically western Europeans's) own growing confidence and sense of self.
Christopher Columbus' voyage to what came to be known as the New World is one such example. Another is Vasco da Gama, who, as many textbooks will tell you, was the first European since the ancient Greeks to cross the Indian Ocean. In other words, da Gama was repeating something that had been done before, yet in that context, it seemed new and unprecedented. It is also of note that the Portuguese da Gama was greeted in Calicut, India, by a Muslim merchant from Tunisia: virtually da Gama's neighbor. In other words, many of the European achievements became exaggerated in Europe and the larger West. As for Columbus, in seeking support for his enterprise after his first voyage failed to get to his destination of India, he sought to sell his project and play up his accomplishments. In short, European accomplishments in navigation were overstated by Europeans themselves and entered western culture in that overstated form.
As a foil to the claim that Columbus found North America, our contemporaries often cite that Leif Erikkson reached Newfoundland and surrounding areas around 1000 A.D.; but how reliable are the Norse sagas? Even if they are reliable, did the Spaniards and other Europeans of Columbus's time know of them? Furthermore, although we tend to see the Caribbean and Canada as belonging to a single entity called North America, there was no such entity by that name. The name America derived from the accounts of Amerigo Vespucci and was initially applied only to what we today call South America. Are Newfoundland and, say, Hispaniola, the same part of the world?
Further, the greatest significance of Columbus' voyage was that it was reproducible and created a bridge between the so-called Old World and New World, which the Norse expeditions had not done. All these issues need to be taken into consideration and explored in more depth before we find a satisfying answer to the above question.