If it was so offensive, both India and China would not be at loggerheads trying to posture themselves as a leader of the Global South.
Simple fact of the matter is that progress in modern world requires networked systems. Europeans and Euro-descendants were able to achieve this networking through racial bonhomie and colonialism. Non-western countries do not have that available to them, so they have to invent new narratives to facilitate that networking.
The fact that India may have orbital launch and Australia doesn't is the reason to reject Developing/Developed dichotomy and move to a different one, Global North/South seems to be the one gaining traction.
Getting offended over the existence of the idea of Global South just because it doesn't hew closely to some arbitrary parameter is similar to saying that G7 is natural but BRICS is dangerous. It's just a statement of rote comfort. If Australia is not a northern country by direction, it's not a western country by direction either; I doubt any Australians are in a hurry to classify themselves as an Eastern society and not a Western one.
