No one has any positive reason to keep him. Only that they don't want another change, because they are worried about some sort of perception issue.
When you have the wrong person then change immediately, like Spurs have done, like Chelsea have done numerous times. We say we want to be a big club and successful but our actions suggest a small club with zero interest in success or even improving. Changing manager is normal, it's not an issue. The days of dynasties like Fergie are over. Replacing underperforming, or unsuitable managers makes success more likely, not less likely.
When this goes even more badly wrong in the run up to Christmas then people will look very silly.