As usual i don't agree with the general feeling about all this.
It is ture that Chelsea doesn't have enough patience with coaches (Ancelloti, Mourinho, AVB and maybe even Scolari).
On the other hand: Chelsea won the CL under Di Matteo, and while they had more merit in it than people give them credit for, they still had a fair amount of luck and won the CL with a brand of football which isn't very attractive.
The big mistake was that Di Matteo could continue.
IMO Chelsea had a disastrous transfer window. Am i totally mad? Maybe. But buying players like Marin (never used), Hazard (i love him), Oscar (he's fantastic) and others is all very good, but they never had any balance in that team.
People always talk about Hazard-Mata-Oscar, and yes they are a joy to watch. Meanwhile Chelsea was weak defensively (look at the match against United and the way United scored the first two goals, that was shocking defending) and could not score goals.
Mikel (who yesterday had a good match, with a pass ratio of 89%) is IMO not good enough. Terry is getting old, Luiz still is a liability, Ivanovic is too slow. That leaves two decent defensive minded players: Cole (world class, arguably the best LB in the world) and Ramirez (fantastic player, but can you consider him a real defensive player? To me he is more CM than a DMF).
On top of that: they don't have a striker.
A team that concedes too much goals and has difficulties scoring goals, is a bad team. Chelsea was overachieving at the beginning of the season.
If they were overachieving, why sack Di Matteo? IMO the team was overachieving despite DM and not because of him.
As a manager he should have seen what happened during the transfer window...either he is responsible for the thransfers or he has no influence on them. In both cases he is a bad manager.
There are rumours that Benitez will be Chelsea's next manager. I'm not so sure about him. There is this story that benitez has fallen out with one of his assistents and that since then he hasn't achieved anything....
The coach Chelsea need is Pep Guardiola. Jurgen Klopp wouldn't be too bad either.