It was stated that Dumbledore understands parseltongue, a language only spoken by descendants of Salazar Slytherin. But Dumbledore is a descendant of Slytherin according to this theory.
It's confirmed not all descendants of Slytherin are parselmouths. Isolt Sayre's mother was part of the Gaunt family, who are descendants of Slytherin. She couldn't speak parseltongue but was able to understand a local horned serpent.
She had two twin daughters, Rionach and Martha. Rionach was a witch and taught defence against the dark arts at ilvermorny. It was believe she was a parselmouth and she didn't want to pass it on so that's why it was believe she was never married. Her twin Martha on the other hand was a squib who married a native no-maj.
Dumbledore's mother was said to have looked native American so it is possible that she is a descendant of Martha Steward. If this theory is true Dumbledore is also a distant relative of Tom Riddle, who is a Gaunt on his mother's side.
It's a pretty popular theory and one of the few theories I actually believe is true.
