European monarchs supported the First Crusade primarily to end Islamic (Muslim) control of the holy land. This motivation was driven by religious fervor, the desire to reclaim Jerusalem, and the belief that it was their duty to protect Christianity. Additionally, supporting the Crusade provided an opportunity for monarchs to gain prestige and power, unite their realms against a common enemy, and divert attention from internal conflicts.
The other options, such as increasing protection of the Silk Road, decreasing the influence of the Pope, and halting invasions of Chinese dynasties, were not significant motivations for the monarchs in the context of the First Crusade.