Social class is an attempt to explain why inequality persists across generations in societies that claim to offer equal opportunity. Whether it does explain this — and which of several competing frameworks explains it best — is one of the most contested questions in social science.
A child born to a surgeon is far more likely to become a surgeon than a child born to a cleaner. This is true in almost every society that has been studied. The question is not whether this happens — it clearly does — but why. Class analysis is the attempt to answer that question. The different frameworks give very different answers, and those answers have very different political implications.