Solving the problem may involve estimating, but blindly being asked "How long will this take?" without exploring the entire solution space, often without even being aware of what problem needs to be solved with that information, is when you get failed results. A time estimate may not even be the right tool to solve the particular problem.
If you are the one asking "How long will this take?" you have already recognized that you don't have a satisfactory solution yourself and need to defer to the experts, so why obscure useful context from those you are deferring to? While there may be some sense of pride in being the one to come up with the solution, such emotions aren't suitable for the workplace. It's okay to give someone else the 'glory' if they have the solution and you don't.
2 weeks with 9/10 fitness is a very different estimate from 2 weeks and a 6/10 fitness. The latter should result in more discussion so those you're giving the estimate to can better understand how likely you are to miss that estimate and what they can do to facilitate a better estimate. "Give me 2 days to investigate this 1 thing that's a total unknown, I can probably give you a better estimate afterwards".
The problem is very few people on either side of that table ever want to do this.