If management is pushing for lower estimates, it's typically going some reason along the lines of:
- Someone higher up gave them a fixed budget or a fixed deadline and they can't exceed that.
- They're expecting market conditions to reward earlier delivery more than higher quality.
- They don't understand the problem domain.
- They do understand the problem domain but don't understand limiting factors like tech debt or organizational process hurdles the developers face that preven them from hitting timelines they would hit under ideal conditions.
If it's one of the latter two, they need to have a come to Jesus moment with themselves because you can't run a team if you don't understand what they do, how they do it, and what obstacles they face.
If it's one of the former two, great, communicate that, but then whoever is ultimately accepting or using your product needs to understand the basic release models that you can either get a complete set of well-defined features or you can get a specific release date but you can't get both, except by luck. And you need to have an organizational culture that isn't going to punish developers if they don't get lucky and meet only one of those goals.
Companies purchasing labor output don't get to violate the basic constraints of being a consumer. If you've got a fixed budget, fine, but you get what you pay for.