This is a great question with a lot of answers. It's true that the idea of Cortez as a deity was never widely accepted by the Nahua and Mexica peoples, but it was a concept that was entertained by some, and indigenous texts describe Moctezuma II fully exploring the possibility. However, these indigenous texts were made decades after the Spanish invasion. Therefore, the Nahua academics who were recording Moctezuma II's actions were probably very young at the time of the invasion, if they had been born yet at all, and therefore everything that they recorded would have been what they learned from the previous generation, most of which had been wiped out by the invasion and the massive smallpox epidemic that followed. As a result, the accounts of the years leading up to the invasion are somewhat unreliable.

Additionally, many of Moctezuma II's subjects were dissatisfied with how he chose to deal with the arrival of Cortez, passively sending them gifts with diplomatic requests to not continue on their journey toward the capital of Tenochtitlan, rather than having them killed immediately. The academics documenting Moctezuma II's actions may have been attempting to explain why he allowed such a dangerous set of men into his land without putting up a fight: if Moctezuma II had good reason to believe that Cortez was Quetzalcoatl, he would be justified in his cautious, non-violent and non-confrontational approach to dealing with the Spanish. Therefore, the belief that Cortez was Quetzalcoatl may have been played up by some of the indigenous academics documenting these events.

Bearing all of this in mind, we can jump into the Nahua mythology of Quetzalcoatl, which was complicated by the politics of the Mexica. Quetzalcoatl was considered the creator of modern Man, and the primary deity of the Nahua pantheon for a long time. He was a god of learning and of wisdom, of craft-making and knowledge. However, around 1430AD, a man named Tlacaelel, son of emperor Huitzihuitl and brother of emperor Moctezuma I, lead the Mexica nobility in a concerted effort to destroy the codices that venerated Quetzalcoatl, and to replace him with Huitzilopochtli, the patron god of the Toltecs and god of war. They would rewrite history and transform Tenochtitlan into a powerful state driven by war and massive blood sacrifice, with the Mexica people directly descended from the revered Toltecs (which, in reality, they were not). I highly recommend further reading about Tlacaelel, who was the architect of the Nahua empire as we knew it upon Cortez's arrival in Mexico.

The codices venerating Quetzalcoatl were burned and rewritten to include the story of his disgrace. The legend of Quetzalcoatl that was being taught in Tenochtitlan at the time of Cortez's arrival stated, basically, that Quetzalcoatl had fled the land after getting drunk and sleeping with his sister, but went on to say that he would return in the year One-Reed (Ce-Acatl). The year 1519, the year of Cortez's arrival in Tenochtitlan, happened to be the year One-Reed. This is the single largest connection between Cortez and Quetzalcoatl.

Before Cortez arrived in Tenochtitlan, he was working his way from the coast to the interior of Mexico, and Moctezuma II was receiving reports from messengers who told him that Cortez was requesting a meeting. Moctezuma II is reported to have sent some of his best knights back as messengers with gifts of the garments and trappings of several different deities, including Tlaloc, Tezcatlipoca, and Quetzalcoatl. When the messengers met Cortez, they dressed him in the finery of Quetzalcoatl, and Cortez is reported to have immediately had them chained up and kept as prisoners (see Miguel Leon-Portilla's The Broken Spears for indigenous accounts of these interactions).

I'd also like to drive home that all accounts of the Nahua believing the Spanish to be deities were created under Spanish influence, after the invasion. The indigenous academics who were documenting the invasion were all being compelled by Spanish men to document their experiences. Usually the intended purpose of these accounts was to better understand the Nahua religious and political history, that the Spanish might gain some understanding of how better to convert them to Christianity.

My sources for this response were Miguel Leon-Portilla's The Broken Spears and Aztec Thought and Culture, and Laurette Sejourne's Burning Water: Thought and Religion in Ancient Mexico.