Final answer:
The Boxer Rebellion was primarily caused by China's opposition to Western colonialism and imperialism, which incited a violent response aimed at expelling foreign influence. The US feared the further division of China and loss of trade opportunities after the rebellion, leading to the promotion of the Open Door Policy, ensuring both trade access and the protection of Chinese sovereignty.
Step-by-step explanation:
The Boxer Rebellion was a significant uprising in China during the summer of 1900, fueled primarily by anti-colonial and anti-Christian sentiment. The Rebellion's causes were multifaceted, including nationalistic reactions against sovereign encroachments by Western powers and Japan, the economic and cultural infiltration through imperialism, and the Chinese government's failure to address these intrusions.
Specifically, the Rebellion aimed to expel all Western influences—which manifested through targeted aggression against Christian missionaries, foreign businessmen, and associated infrastructure—and to rid the country of what the Boxers perceived as corruptive foreign elements.
Following the rebellion, the United States feared further partitioning of China by European powers looking for compensation for their losses, which would threaten American interests in the region. To avert such division and to assert American influence, Secretary of State John Hay advanced the Open Door Policy that emphasized the preservation of Chinese territorial and administrative integrity while enabling free trade.
In response to the Boxer Rebellion, the US, alongside other nations, deployed troops to quell the uprising, ultimately demonstrating its commitment to a strategy of protecting and expanding its economic interests through the Open Door principles, which persisted until the shift in China's political climate post-World War II.