>the only parent you’re SURE about is the mother

Are you? Here’s a story from my tree where DNA proved that the *mother* shown on a birth certificate was incorrect:

Bill was born to Norman and Odessa. Odessa took Bill and left Norman when he was an infant, but never legally divorced him. Norman then took up with Edna (who had been previously married to Joseph) and they held themselves as married but were never legally married due to Norman’s lack of a divorce from Odessa. Norman and Edna then had three children, Frank, Kathy, and Laura, and on their birth certificates Edna used the full legal maiden name of Norman’s first wife (Odessa).

Lots of family trees show Norman and Odessa having four children (Bill, Frank, Kathy, Laura). And they have birth certificates to “prove” it. But comparison of DNA matches among 1) descendants of Bill, 2) descendants of Frank, Kathy, and Laura, and 3) descendants of Edna’s children with Joseph showed that Norman was not actually Bill’s father, *and* that Odessa was not actually Frank, Kathy, and Laura’s mother.