The question of why Voldemort was considered the heir of Slytherin requires an understanding of the history and mythology of the Harry Potter series. To answer this question, we must delve into the origin of the concept of the heir of Slytherin and the role that Voldemort played in this context.

The concept of the heir of Slytherin first appeared in “Harry Potter and the Chamber of Secrets,” the second book in the series. In this book, it is revealed that the Chamber of Secrets was created by Salazar Slytherin, one of the founders of Hogwarts School of Witchcraft and Wizardry, who believed in the superiority of pure-blooded wizards and witches. According to legend, Slytherin placed a monster inside the Chamber that could only be controlled by his true heir, who would be able to use it to purge Hogwarts of all those who were not pure-blooded.
In the book, it is revealed that the monster in the Chamber is a basilisk, a giant serpent that can kill with its gaze. The basilisk is released from the Chamber by someone who claims to be the heir of Slytherin, and it is up to Harry Potter and his friends to stop it.
So, why was Voldemort considered the heir of Slytherin? The answer lies in Voldemort’s lineage. Voldemort was descended from Salazar Slytherin himself, which made him the last living member of the Slytherin family. This lineage gave Voldemort a claim to the title of heir of Slytherin, and it also gave him a special connection to the Chamber of Secrets and the basilisk inside.
Furthermore, Voldemort’s ideology aligned with that of Salazar Slytherin. Both believed in the superiority of pure-blooded wizards and witches, and both sought to rid the wizarding world of those who were not pure-blooded. Voldemort saw himself as the true heir of Slytherin, and he sought to use the power of the basilisk to further his own goals.
In addition to his lineage and ideology, Voldemort’s actions also cemented his position as the heir of Slytherin. He was responsible for the opening of the Chamber of Secrets during his time at Hogwarts, and he was the one who released the basilisk. These actions demonstrated his control over the Chamber and the basilisk, and they furthered his claim to the title of heir of Slytherin.
Moreover, Voldemort’s connection to the Chamber of Secrets was also strengthened by his possession of one of Salazar Slytherin’s prized possessions: a locket that contained a piece of his soul. This locket, which was one of the seven Horcruxes that Voldemort created to achieve immortality, had been passed down through the Slytherin family for generations. Its possession by Voldemort furthered his connection to Slytherin and his claim to the title of heir.
In conclusion, Voldemort was considered the heir of Slytherin due to his lineage, his ideology, his actions, and his possession of one of Salazar Slytherin’s prized possessions. These factors combined to create a powerful narrative that linked Voldemort to the history and mythology of the Harry Potter series. While Voldemort’s claim to the title of heir of Slytherin was ultimately rejected by the wizarding world, his role as a villain in the series was enhanced by his connection to Slytherin and the Chamber of Secrets.