""" I do not know how to develop a meaningfully accurate number of days or hours that this will take. The software industry as a whole has not developed reliable best practices for estimating software tasks or for teaching those practices to other software engineers. As such, it would be deceptive and unprofessional for me to give you a number. """
To really communicate this effectively, you have to say it with confidence: standing up straight, shoulders back, making eye contact. It is uncomfortable and the sort of thing that makes me feel a bit nauseous to say, but as a professional, it is important to be honest even in the face of discomfort. To this opener, I would personally add to this statement either
"However, if you are looking to get a rough assessment of the size or complexity involved, this is the sort of task that I can take 2 hours and produce a breakdown of the components of this."
or
"I sense that what you'd really like is a judgement of how large or complex this task is. However, at this stage, the task is not well-scoped enough for me to do that. I would need to invest effort into fleshing that out. If you'd like I can timebox one (or two) days to investigate and report back with what I discover are the major components to this and whether there are likely to be more unknown components."
or
"In particular, this is the sort of task where the work to discover the problem and the correct approach to solve it is 90% of the battle. There unfortunately isn't a way to break that down ahead of time."
Depending on whether it seemed like a task similar to one that I'd done before or not--or whether it was a bug-hunt.