The Eagles should have fired Chip Kelly much earlier actually. He traded away and let go of all his star players and because of it, the Eagles had a terrible season. His philosophy severely failed, and as such the Eagles were well within their right to fire Chip Kelly. If he had succeeded it would have been a different story, though.
Very few college coaches have what it takes to be successful in the National Football League. Chip Kelly became the latest victim on the list of college coaches who just couldn't cut it in the NFL. His season with the Philadelphia Eagles has been terrible in a nutshell. He has also made numerous questionable calls that do not sit well with wealthy NFL owners who want results.
There are many fields of employment where an employees job depends on their productivity and ability to meet company goals. NFL teams are huge money-makers, and of course their company goal is to win. If a coach, or leader, can't get with the company goals and make things happen, and that's a condition of their employment, then they should be let go.
He brought in an entirely new system to a team that has never won a Super Bowl. It hasn't worked yet, but three years isn't long enough to know if it is going to work. If they can't commit to implementing a new system and rebuilding their team they shouldn't bother continually changing coaches.