He stated that he hoped that his clock by running backwards might cause his boy to come back. He did, but just not the way he thought it would.
WMG / The Curious Case of Benjamin Button
Benjamin is actually the reincarnation of Mr. Gateaux's son whom he lost in the first world war.
Benjamin's curious case wasn't actually unique.It wasn't just Mr. Gateaux's clock, or its maker's wish for his son to come back to him, that caused Benjamin's condition, but the collective wishes of people all over the world that time would reverse itself and bring back their loved ones! This global desire becomes so intense in the wake of tragedies like the Great War that it causes hundreds of such births; however, not all the ancient-looking babies survive to get any younger, and those that do live a long life choose to keep their circumstances every bit as private as Benjamin did, fearing they'll be treated like freaks. The reverse clock re-starting at the end is a metaphor for how Hurricane Katrina will also trigger one or two such births.
Benjamin's official cause-of-death was heart failure by tetralogy of Fallot.Most of a fetus's blood flow bypasses the not-yet-breathing lungs, passing instead through an opening (foramen ovale) between the heart's atria and a temporary branch of the pulmonary trunk, the ductus arteriosus. Normally these passages close up when the newborn takes its first breath, after which blood flows alternately between the lungs and the rest of the body. If neither passage closes properly, the lungs receive insufficient blood and the baby rapidly becomes cyanotic: a congenital heart defect called tetralogy of Fallot. As Benjamin's body matures in reverse, his heart would've developed a weak spot between its atria and a growing, sealed ductus arteriosus in his final weeks of life; at the end, both these passages opened up at once, his lungs (although air-filled) lost nearly all their blood supply, he closed his eyes in sudden exhaustion and his skin turned blue as Daisy covered his "sleeping" face.
Benjamin's maternal grandfather was Orkan.Orkans age in reverse, so it stands that Elizabeth Abbott-Button was half-Orkan and gave the aging trait to Benjamin.