Football is a business and the Philadelphia Eagles may have wanted to reduce costs, the Eagles may have grown tired for his demands for more money, and I am sure the Eagles would have prefered to have trade them.
The Coach Chip Kelly recently said he had no problem with DeSean Jackson so I would say that puts in doubt the rumors of him not getting along with coaches. If he fell a sleep in a meeting I am sure that was dealt with.
Questioning his work ethic is hard to do when you look at his production. DeSean Jackson is a three time Pro-Bowl receiver. He is a proven playmaker. Last season he caught 82 passes for 1332 yards and 9 touchdowns. He has had 1000 plus yard seasons three times in his six year career. In addition off the field he hasn't had any incidents. He runs a charitable foundation. Both of them should speak volumes about his character instead of rumors.
The Redskins were willing to take a risk by signing him to a three year deal for 24 million dollars and two of those years guaranteed. I heard some random talking head say they would only sign DeSean to a one year deal so Jackson could prove himself. The Redskins took the risk and signed him. Washington improves their team which is important since they didn't have a first round pick.