Bum Phillips had been a successful coach in Houston and was hired by New Orleans in 1981 to turn the franchise around. The Saints had the first pick in the 1981 draft. George Young really wanted Taylor, who he thought could be the greatest linebacker of all time, but never publicly indicated any preference.
Phillips had had a lot of success in Houston with Earl Campbell and wanted a big back to build the offense around in New Orleans, so he picked Heisman Trophy winner George Rogers.
Ed Croke, the Giants' PR director, was at the Giants' table at the draft. Young had told him to prepare two cards, one for Lawrence Taylor and one for George Rogers, and, when the Saints picked one, send up the card for the other as fast as he could. So Taylor became a Giant.
Rogers was not a bad pick - Offensive Rookie of the Year, two pro bowls - but with him the Saints were never better than 8-8. After four years, he was traded to the Redskins, where he led the league in touchdowns in 1986 and won a Super Bowl Ring. However, Young got the player he wanted, and LT proved him right.