He's not Woke enough for the beeb they won't touch him with a bargepole. Which is why he got cut adrift in the first place passed over for other jobs he should have walked into like chair of QT. He's not even a Guardian reader for chrissake! Utterly beyond the pale.
He had one of the cushiest, best paid (for the hours involved) and lowest commitment jobs in the BBC news/current affairs department, and had massive amounts of leeway compared to most due to his position and seniority.
He left because he wanted to not abide by the BBC's impartiality rules, and because he was offered a huge payout at what he was expecting to be probably the last major onscreen job of his career, where he would be able to set the rules and feel of the program and to not be held to the BBC's impartiality rules.
He gambled on GB news being what he wanted, and found out that the people putting up the money wanted to take it far further and to a much lower quality than he was expecting, so that rather it being the shining end to his career, it was a laughing stock that made a mockery of what his career and showed exactly how bad it can become when you try leaning as far to one side of the political spectrum as you can under UK broadcasting laws, whilst not wanting to spend any money on the actual news gathering side of it.
At the BBC he had access to the resources of one of the best news gathering organisations in the world, and the ability to choose how he used them, at GB news it appears he was the respectable face of a bunch of clowns with an agenda and no actual resources given to news gathering (or technical staff, presentation staff, researchers, archivists, editors or any of the 101 different people that work behind the scenes to make someone like Neil look good in front of the camera).
In short if you think he was pushed out of the BBC, I've got a bridge to sell you.