Why is the story that Parmenides invented logic considered a legend?

The medieval tradition claiming that the Greek philosopher Parmenides invented logic while living on a rock in Egypt is considered pure legend.12

While Parmenides was indeed the first philosopher to utilize extended arguments to support his views rather than simply presenting a vision of reality, this practice is distinct from the formal study of logic. Parmenides never systematically formulated or studied the principles of argumentation in their own right, and there is no evidence that he was even aware of the implicit rules of inference he employed.12

In contrast, the systematic study of logic is credited to Aristotle, who established a formal system of rules and strategies for reasoning. Unlike his predecessors, Aristotle was the first to use variables, allowing him to reach a level of generality and abstraction that defined the discipline.3