A short taxonomy:

Stupidity: Having no native ability for thought at all.

Idiocy: Being able in one thing but incapable in all else. 

Ignorance: Not knowing where to start due to lack of information. 

All suffer from ignorance at every juncture of life; a good many are idiots having over-focused on only one possibility; a few are stupid, and that being the case, have no idea really.

The stupid are unteachable by nature and one can have some mercy toward them. But idiots are unteachable by choice and create a woeful ignorance that will never become informed enough to get going in a positive direction. 

The willful ignorance of idiots arises from being wrongly convinced that success achieved in their one area of obsession/expertise means they must know something about being successful in any other area.

The willfully ignorant should never be tolerated.