One big insight for me, which you obviously put to use in your story, was learning to give a different number.

"I don't know" is understandably frustrating to people who are trying to plan work and answer requests. They often respond to that by pushing for a delivery date even when it won't be accurate, but a lot of the time what they fundamentally want is a numerical answer. "I'll have it scoped out by Tuesday", "I need at most 3 days to learn enough to estimate", and so on all aid that planning without committing to a project timeline. That rarely ends the conversation, just as it didn't in your example, but it does a lot to show good faith and justify not answering the initial question.