One of the things people like to use against Bill Parcells is that they call him a "quitter."
He's resigned from all of his coaching and executive positions, either due to personal or health reasons, but him leaving has left a lot of NFL people and writers with bad tastes in their mouths.
Like, for example, after the Giants won Super Bowl XXI, Parcells was talking with the Atlanta Falcons about their head coach and general manager vacancies and might have actually taken the job if not for then-commissioner Pete Rozelle stopping it.
After he won Super Bowl XXV, he retired citing health problems and did work as an announcer. However, less than two later, Parcells had an agreement to become the next coach of the Tampa Bay Buccaneers, but backed out at the last second.
Not only did Parcells irate the city of Tampa, but because Ray Handley was such a failure, Giants fans were a little irritated that he was looking to coach elsewhere after retiring not too long ago.
Tom Coughlin, on the other hand, has been impossible to get rid of.
He's been on the hot seat in New York a few times. In 2006 after they went 8-8, a lot of people thought Coughlin would get axed because he had lost the locker room and there were a lot of whispers that Bill Cowher might be the next coach in waiting.
Coughlin changed his attitude toward his players and won back his team in 2007. They also went 10-6 and won Super Bowl XLII that season as well.
In 2011, they had lost four straight and dropped to 6-6. Everyone thought Coughlin had lost it, and if they had lost a fifth straight to the Cowboys, it really could have signaled Coughlin's end. Instead, they won the game against Dallas, won their last two to go 9-7, and then won Super Bowl XLVI.
Coughlin has always wanted to be the Giants coach and has never expressed any interest in leaving. It's what has made him so popular and beloved by the fans today.