So that they can say it was by mutual consent, which always reflects better on the person being shit-canned. Not that his opinion really matters. They could have easily kept him in the job.
Nothing to do with mutual consent making him look good. He couldnt look any worse.
It isnt Allardyce offering to work for that company for a fee that has lost him his job. It is the fact that he has offered to show them how to get round rules his employers have had and boasts about doing to for years.
He wasnt looking to run it past the FA if he was ok to give information to flout those rules or run it by them that they are ok he has done it in past.
If this was just Allardyce looking for £400k to work for an overseas company he wouldnt be getting sacked.
They were correct to sack him and Allardyce knows it was his fuck up.