"Growing balls" was mentioned, but that's mostly a problem of the manager, who has pressure from above and lets himself being talked into promises that he cannot keep. At my workplace things got improved a lot when my manager's manager, who never managed to get the results he promised, was replaced. The new manager was given a list of 10 things to achieve, and he just said "no" to seven of them. And didn't budge one bit from the seven "no's" no matter how they tried to pressure him. And then the teams under him, without ridiculous deadlines, achieved the three tasks he had accepted. Which the previous manager would have failed to do. , Everyone (up and down) is really happy with him.
What bad deadline setting achieves is: Pointless stress, drop in productivity, feeling bad because everyone fails, possibly rushed and low quality products.
What you can achieve with deadlines: Change priorities so that some tasks will be finished. For example, if job A looks like it will be 90% finished, and job B looks like it will be 60% finished, you move effort from B to A so that one of them will be done within the deadline. Or reduce the scope of a job. If job A with all planned features cannot be achieved in the deadline, you reduce the features.
About estimates: If you make a best estimate for the time a task takes, and you are really, really good, then the task will take the estimated time, plus or minus some random extra time. That's why it is called a "best estimate". If you make an estimate, nobody can change that. Never allow anyone to make you change your estimates (unless they first reduce the task that is estimated). Your manager then can set targets. If these targets don't agree with the estimates, that's his fault. If you estimate "it takes three months" and he says "do it in two weeks", it's his fault if you don't finish in two weeks. It's even more his fault if he stresses you out and you don't even finish in the estimated three months.