> I'm not sure how to avoid answering these loaded questions though. In my experience trying to 'negotiate' with people like that: they will just ask you the same question in 5 different ways and it will eventually get so uncomfortable you'll tell them anything to move on.
Once you realize what's going on, you can turn that into a game.
Do you know the game where somebody asks you a bunch of questions, and they you allowed to answer with anything except "yes" or "no"? It's very hard to do, because it's such an ingrained habit.
If you really want to not give an estimate, make it a game to not give one.
But, give them something else instead. Work out a bunch of questions about uses cases / data volume / whatever, and say "if those were answered, we could build a prototype in a few days that would let us make a more reliable estimate" or something like that.
Another comment: coming up with good estimates is work. The other day somebody asked me if I could come up with a rough estimate for a (poorly specified, IMHO) project, and my answer was: no, I don't have time. If you need it anyway, formulate it as a task in Jira, so that it gets prioritized along with all my other work.
(Fun fact: we estimate our tasks in story points, so then we estimated how much time it would take us to come up with an estimate... :D )