Sticking to your guns

People will often interpret a difficult problem as being impossible to solve before they have considered all possible solutions, spent sufficient time on it, or thought about it in an efficient way. Often, the person will also be a pessimist, and will therefore be inclined to declare a problem inherently insoluble all but immediately.

This would not be a significant problem on its own. It would be easy to find solutions, explain them, and solve the problem. It would also be easy to explain to the person, perhaps after solving a few problems for them as a demonstration, how to think better and solve problems more efficiently.

The real problem arises when they wish to maintain that the problem is insoluble despite proposed solutions. This seems generally to be a case of sticking to their argument and not wishing to be shown to be wrong. So even when you propose a solution, they will insist that it will not work (often for self-imposed emotional reasons), rather than being optimistic and trying to find ways to make it work.

Pessimism is very dangerous; it makes us self-sabotage.