I have produced estimates for almost 20y now, and boy do I hate that. There's multiple layers to it.
This post touches the nefarious one. Sometimes yes, someone wishes something would come sooner and will shake the tree to see what happens. Sometimes there's actually a reason for it - be it budget, customer related, event related, etc. Sometimes someone knows better, because the feature or project is similar to another that was shorter.
When someone discusses estimates with an underlying motive other than their experience and surprise at the cost, I usually enter a discussion where I produce the evidence for our numbers and justify what we are telling.
It highly depends on why we produce estimates in the first place. If it's for budget or planning, I couldn't care less to reduce estimate, since these exercises are pointless in nature in my experience (the budget or planning is usually rendered moot within weeks of being approved).
If its to predict delivery dates, I'm usually very conservative, note that I am not in the art of divination, and that reducing estimates is a risk in itself if anything bad happens. When people are acting on bad faith, documenting stuff usually tames things a little. Unless things are very simple and predictable, I also usually provide several dates with confidence indices. This is a framework that's much harder to negotiate, and give some information to whomever "needs" those dates. It helps reducing the pressure a bit while being non committal and leaving room for error (and I never give a 100% confidence).
TBH, I don't think I've ever been in trouble for "being late", especially because I have always been able to explain that we weren't late, we just gave an incorrect date in the first place.