Don't want to pick on you as you're new, and some of these points have been voiced elsewhere. To be clear, I don't think ETH is going to be here next year adn I think he knows it. But these sticks people are beating him with..at least get the facts straight.
1. Antony is his fault. The fee is not his fault. If Antony had cost what he should have (less than the two players you mentioned) I think people would be more okay with it. ETH identified Antony early, the club waited til the season had started, panicked, and hugely overpaid. That is nothing to do with ETH. Similarly, I've seen nothing whatsoever to suggest ETH wanted Casemiro. There were no links, no rumours, nothing until the moment we went into panic mode and presumably Case's agent came calling. Those two combined are almost half the spending ETH gets abused for. You think ETH wanted players only available on loan? Are you serious? Of course not. And the De Gea argument? You go ahead and let me know how he's getting on with his new club then. Admittedly, he's not conceded many goals this year!
2. We had no fit CF for the first month of the season, our non-creating right-winger was avoiding the Brazilian police, our other right-winger was engaged in a tantrum and our key goal scorer from the season before seems to have forgotten that he likes football. The great savior from fans (Amad) wasn't fit. ETH's new, highly mobile, energy-driven midfield of Mainoo and Mount weren't fit. So, erm, who is it that was supposed ot be doing the scoring?
3. Garnacho runs his heart out every match, you think he's downed tools? Sancho is not thriving in the Bundesliga, he's played 15 times and has 2 goals and 2 assists. In the Bundesliga, where goals come free. I'm not sure of evidence that ETH is causing the injuries somehow, but he obviously did not cause Martinez's, did not cause Malacia's, did not cause Mount's and so forth because these players aren't even playing. Varane gets injured if he sneezes, and did before ETH.
Again, I just challenge people to consider what another manager would do with the players actually made available to him. He's culled off over 23 first teamears since he came in, and brought in barely 10 (not loanees). His great tactical plan was mobility and energy with Mainoo and Mount, and both have missed huge chunks of the season. He wanted a senior CF to lead the line (called Harry Kane) and was given a kid with barely a season of top-level football in him. He is using Ole's first XI with a couple of kids and a new keeper. There is no mystery full back he can call on, or mobile defensive midfielder, or even a substitute centre forward. Look at our bench the last few matches.
If your argument is that ETH is causing these injuries, that's a good reason to turn against him, but I'd love some evidence of that. Otherwise, a manager has to deal with the team he has, and this team, with these injuries, is toast. It's mid-table. And we are.