The term 'west' outdates the discovery of America and no longer has anything to do with Geography. It used to mean western Europe. Now it essentially means western Europe, canada, australia, and america. All of which have cultural roots in Western europe and liberalism etc.
Yep, and "South" is a somewhat archaic term to refer to developing countries. Australia is not of the "South" despite being in the southern hemisphere.[1]
It's also weird to refer to the Asian countries north-west of Australia as "Far East"; though that usage is also fading.
'western' means 'west european and similar', not 'western hemisphere'. It basically means most of europe (now) and the anglo 'new world' countries, though the exact countries involved vary depending on who is doing the defining.