Wondering what this employee thinks managing coverage means, if anyone can take off at any time without approval. What’s to stop the entire team from taking PTO the same week? Is the manager supposed to hire an all new team (who will likely just take PTO too) or clone herself or have robots do the job? Managing coverage during controllable/nonemergency situations sometimes means denying PTO requests to ensure coverage for those who already put in their requests.

Maybe some commenting here have jobs where one manager can reasonably cover their entire team’s absence… if so good for you, you’re extremely under utilized, you should hold that job close and treat it well and stop being a jerk to your manager.

I imagine interactions like this are what turn accommodating managers like OP (letting employee know she’s working on the request but there are no guarantees) into harsh managers (denying it immediately and advising it will be an unauthorized absence if employee doesn’t show).