Why all Ores are minerals, but all minerals are not ores?

Ores are minerals from which metals can be extracted conveniently and profitably. Let us take the ore of aluminium, that is bauxite.
Minerals are substances from which metals cannot be extracted conveniently and profitably. For example, Kaolinite is a clay mineral of aluminium. But it is not an ore because aluminium cannot be extracted profitably.
Hence, we can conclude that all ores are minerals but all minerals are not ores.