Final answer:
European nations assisted the Qing government in suppressing the Taiping Rebellion mainly to protect their profitable opium trade interests in China, as the rebellion's leader, Hong Xiuquan, enforced a ban on opium.
Step-by-step explanation:
The reason European nations helped the Qing government put down the Taiping Rebellion was primarily due to their economic interests in China. European powers, especially Britain, had just defeated the Qing Dynasty in the Opium Wars and were benefiting from the opium trade in China. The leader of the Taiping Rebellion, Hong Xiuquan, not only had a radical approach to Christianity which could potentially alienate European sympathies, but more critically, he implemented a ban on opium use, directly threatening European economic interests. Thus, rather than a desire to end famine, the opium trade, or any alleged alliance between the Taiping and the U.S., European involvement was largely motivated by the maintenance of their lucrative opium trade. Moreover, Hong Xiuquan's violent approach and internal divisions within the Taiping further weakened their cause, making European-supported Qing forces successful in ultimately suppressing the rebellion.