Essentially, sailors rejected oppressive authority, left that authority, found paradise on earth and began living there. (That's the basic story of Mutiny on the Bounty! A true story.)
Years later, civilized(?) authority discovered people living in this paradise and decided to control it. (Pitcairn is in the Pacific Ocean. Great Britain is in Europe. Great Britain owns Pitcairn now.)
Pitcairn families were minding their own lives when GB came along and fucked things up.