European nations helped the Qing government put down the Taiping Rebellion primarily because they were concerned about the potential destabilization of China, which could negatively impact their economic interests, particularly in trade. The Taiping Rebellion threatened not only the Qing Dynasty but also the relatively profitable trade routes and concessions that European powers had established.
While the reasons you mentioned might touch upon some aspects of the broader context, none of them fully capture the primary motivations.
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Europeans wanted to end the famine caused by the Taiping: While the rebellion did lead to famine in some areas, European interventions were less about humanitarian concerns and more about stability and trade.
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Europeans wanted to end the opium trade of the Taiping: The Taiping Rebellion did indeed oppose opium, but stopping the trade was not a primary goal of European intervention.
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Europeans wanted to end the alliance between the Taiping and the US: There was no significant alliance of this nature; European powers were more concerned with their own interests in the region.
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Europeans were angry with the Taiping for banning all drugs and alcohol: The ban on opium and alcohol did not motivate European intervention; rather, their focus was on maintaining their economic foothold in China.
In summary, the main reason for European intervention was the desire to maintain stability and protect their economic interests in China amidst the chaos of the rebellion.