I'm going to go out on a whim here to defend him a bit, seeing as so many think he is just shite and some think Ole was better, as if it's fair to compare an interim stint with no backing to a cultural reset over three years with backing.
When he joined he said absolutely the right things, he tried to get the team to play a high intensity pressing game and it genuinely looked plausible that this could be done, somewhat (notwithstanding his pregnant joke), after seeing that for a third of his first match. He obviously ruffled a few feathers from the get go in terms of team selection, in what was already a poisonous dressing room. It was not on him, and he did not expect Carrick, McKenna and Pert to all leave, leaving him with a major headache of getting in good enough coaches in the short-term, guaranteeing that there be no feeling of continuity, just a substitute teacher vibe. He managed to make us tighter at the back and we consistently performed below our xG for a long while, which was 100% on the players being profligate. He at least got us creating chances, more chances than the opposition. I don't know the politics of the January window, but he clearly wanted options and got none, whether he signed off on Martial going on loan as he was a moody feck around the camp, I don't know. But he wasn't to know Greenwood would turn out a wrong'un and that Cavani would only be fit enough to play for his country. So he was pretty much left with Sancho, Elanga and Ronaldo, with Rashford on a hiatus from being a footballer (his form has been far too diabolical to be excused as needing an arm around the shoulder). Come Atletico, we played terribly in the away match but somehow fluked a draw, but as soon as we got knocked out of the CL there was clearly no appetite left, what with Pogba declaring the season dead, which shows his professionalism.
Rangnick went ballistic in the pressers, which obviously alienated the players further, but that made sure there would be no papering over cracks. The frailty of this team was exposed for all to see. On the eve of the game at Anfield he went no holds barred and laid down the gauntlet for the players to react, to show some backbone, and they had none.
If this had been about self-preservation and nothing more he'd have stroked their ego relentlessly to ensure top 4 and he might have achieved that and in the process we'd be looking at minor augmentation in the summer, as oppose to a rush to get to a clean slate.
It's really impossible to compare a manager given three years and 100s of millions in backing, versus an interim period when everything has gone to shit (much more so than when Ole joined, I mean 4-0, 5-0, 4-1). That being said, Ole declared "we're a fantastically run club" while Rangnick called it how it is. That difference is enormous, to Rangnick's credit.