In "proper" mathematical use, only axioms should be called intuitively obvious. Everything else must be proven rigorously. However, I, being a mathematician of sorts, look at a simple word problem, and think, "you just do this and the answer jumps out at you. Why can't you see it?"
Or, in problems with a little more information than is strictly required, "what do I do with this number?"
"You just ignore it! Why is it so difficult to understand that someone might give an extra number for you to worry about?!"
It can be very frustrating when someone you are trying to talk to cannot see what is intuitively obvious to you.
I never understood why word problems are so often considered the most difficult part of mathematics, when they are a step away from the abstraction that makes math hard.