Totally agree with you. My point was that although he was fired-he engineered his dismissal. It all backfired on him quite deliciously and continues to do so. His post match 'sit down' press conference shows a broken ego. His talk of 'need a miracle, something unique' was like watching a car...
The outcome was controlled by TB, we all can see that. And yes, he was fired but Poyet was only left with the getting fired option so he engineered it himself-a resignation in all but name.
He most certainly did choose to leave.
He himself engineered his departure. He may well have been sacked but that was exactly what he was looking for so he could get a payoff after his earlier in the season resignation was rejected.