Part of the issue is that most people know the history of the Three Kingdoms period from reading the Romance of the Three Kingdoms, which is basically historical fiction. In RotK, the author has a notable bias in favor of the faction of Shu, which includes Liu Bei, Zhuge Liang, and Guan Yu, among others. As such, many of their feats and actions are glorified, as opposed to that of Cao Cao, for example, who is depicted as a treacherous, villainous opportunist.

Guan Yu was portrayed as being steadfastly loyal to the point of almost absurdity. This is due to a period when he was separated from his sworn brother, Liu Bei, and was forced to seek shelter with Cao Cao. During this period, according to the RotK, while he served Cao Cao, he was continually looking for news to return to Liu Bei. Despite Cao Cao's gifts, praise, and efforts, Guan Yu eventually returned to Liu Bei once he found him. Yet he also remembered that he owed a debt to Cao Cao, and spared him when he supposedly had him cornered (whether or not this actually happened is unlikely as I only know of RotK telling this version of the story).

In reality, Guan Yu had his own flaws, which are not covered in the RotK. He was quite pig-headed and stubborn as well. Similarly, Cao Cao, who was villified, was portrayed in the Sanguozhi history as being a fair administrator and a skilled military leader. But a lot more people have read or watched the RotK than other, more accurate histories, and so the popular conception of Guan Yu as an honorable and loyal remains to this day.