Why doesn't my boolean difference modifier work? OK, I have a long, thin cube. I want to cut a spherical shape out of the bottom. Here is the cube and sphere:

Here's what happens when I add a boolean difference modifier to the cube, with the sphere as the target:

Here are my modifier settings:

Why does it just make the sphere fuzzy instead of removing the overlap from the cube? Why does something so simple have to be so frustrating?
Booleans are very powerful tools but they are very picky about overlapping vertices and edges.
In this case you have a sphere with a top and bottom vertices which have a lot of connecting edges. Top vertex can be seen in attached image. Your boolean will break if the side of your object overlaps with any of these edges.

You could change you sphere to a round cube which doesn't have similar vertices on top and bottom. (To add a round cube use an build-in add-on Add Mesh: Extra objects). Round cube is easier to align with your object. Just make sure none of the vertices and edges overlap.