So let's look at this rationally:
Reasons to let him go =
setting new unwanted records regularly- guilty as charged
Looking tactically inept in most matches- sometimes, although some interesting ideas that work (Liverpool FA cup game for instance, Newcastle at home with the false 9)
No clear style of play- not guilty- there's a clear plan: press high, super fast transitions and overloads, balls played into space for forwards to chase. It's just not a very good plan with a lot of these players unsuitable. Would it be better with more suitable players? I'm honestly not sure and would be fine with anyone doubting this. But it still is a plan and it isn't right to say he doesn't have a clear style of play. It's just not a very good one right now.
Plays Rashford 90% of the season even though he looks awful- Guilty BUT when your senior striker scored 30 goals last season you can see why he wanted to play Rashford into form, especially with three very young and inconsistent forwards (Amad, Garnacho, Hojlund) one permanently injured forward in Martial and Antony who is shite in getting goals. I can see why he stuck with Rashford. It's a just a shame this confidence that he'd regain form was misplaced.
Plays Amad 0.5% of the season even though Antony looks awful- I think Amad was vying more for Garancho or Rashford's position wasn't he? Antony has not been a first choice player for the majority of the season either. Being angry with him for not picking Amad is fine but i think Garnacho/Rashford are the players he mostly picked instead.
Often gets embarrassed by other PL sides, including ones that we should be breezing past- Guilty
Seems to think he's doing great- Not guilty- said many many times it's unacceptable but is confident for the future.
Constant excuses- 50-50 on that one. I can see why people are angry though. Injuries have been ridiculous though.
Reasons to keep him:
We've had a lot of injuries. Correct
Saves money. Correct
Matches Liverpool and City's managers in hairstyle. Correct, but i prefer Poch's luscious hair.