Obversa has a well thought out article that goes in deep to explain his idea.

My theory is that Dumbledore didn’t “learn” to understand Parseltongue…but that he can understand it, because he, like Tom Riddle / Lord Voldemort, is a distant descendant of Salazar Slytherin. He inherited (part of) the Parseltongue gene.

[Harry Potter] How Dumbledore can understand Parseltongue. from FanTheories

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Rosalita Moog (curated content)