The point is that Adian was already skating with a back injury for the entire season and she acts as if it was just a behavioral issue.
He came to the competition in the state which caused that skate. He was kind of provocative during the practicing process.
Not one word about the physical issue, and then she yelled at him after he got off the ice in visible pain. No sympathy whatsoever. And a total refusal to take responsibility for the fact that she might have contributed to this problem that now has his entire career in jeopardy. It's not comparable to Tarasova skating with a cut on her leg, but since you brought it up, Nina Mozer in almost every interview expresses her concern about the health of her skaters. She has empathy, which costs nothing, regardless of how strict you want to be as a coach. But Eteri ignores the elephant in the room and doesn't seem to care about her skaters' health at all. Only who gave her flowers when they left.

Let's not forget that Adian wasn't the only one who left with such issues...sure, these things can happen to anyone with any coach, but Yulia and Polina S. (and maybe Polina T., we'll see) and Adian isn't a very good track record, considering they were all still at the very beginning of their senior careers.