Why do solids not mix well, but gases and liquids mix easily in most cases.

Well, because solids are ... solid. When you mix things together like to make a cake, the ingredients are either very small solids that dissolve or liquids.

The molecules in solid matter are linked to each other by bonds, as if they were glued to each other. Hence, it's hard to move them.

In liquids and gases however, such bounds are way weaker, and thus they move a lot more, enabling us to mix them.