It means they worry about losing their job when they're criticized. Like most things, it was supposed to mean actual physical danger, or at least real mental danger, but now it just means anything that threatens them in some way.
It's ironic, because that feedback could help make them better at their jobs and keep them from being fired. Instead, they force a situation where their termination is completely out of their control.
Frankly, losing your job IS an actual physical danger and a real mental danger. No income, no insurance, have to play the interview game again... Time running out, savings getting gutted (too bad COBRA costs are so high). If you can't find work, well homelessness is a very real possibility (there goes years or decades of equity). There isn't a 'limit' to how far we let people fall, and that's a shame.
I would absolutely expect people in this environment to fight tooth-and-nail for their jobs, and that might result in this kind of resistance to suggestions. Gotta keep yourself and family healthy first and foremost.
One way is to reject all criticism and attack anyone who dares to try, hopefully preventing future criticism so that maybe, just maybe, your boss won't notice your incompetence.
Another is to accept the criticism, get better, and then not have to worry about your job because you do it well.
If someone isn't capable of actually doing their job, they can't really pick the second choice. In that case, it's in everyone else's best interest to expose the situation and stabilize the company, saving their own jobs.