> Why would the CIA actively help the chinese government?

The CIA was running large segments of both sides of the uprising that resulted in the Mossadegh government being swept out of favor and replaced by autocratic rule by the Shah of Iran.

The involvement of the CIA on one side of a conflict sometimes isn't to make that side win, it is to assure that that sides behavior fits an intended pattern which serves the desired outcome.

In general, the CIA or any similar agency might "help" any government to either commit, or appear to commit, an act which is nominally "against" a popular movement, but which (through heavy-handedness, brutality or some other characteristic), ultimately provokes outrage, turns worldwide opinion against that government, and weakens its position or ability to get things done, or even, topples it. I'm suspicious this was done to Mubarak in Egypt and Yanukovych in Ukraine.

The CIA is not a monolithic entity. Different people have different goals & factions develop.

Another question to ask is how did China receive technology transfers from US corporations? This is against the sovereign interests of the US yet it occurred with the cooperation of Americans in various agencies & corporations.