Imperialist supported the Spanish-American War because it would result in America spreading their political and economic power.
The Spanish-American War saw Cuba fighting against Spain. In this case, the US took the side of Cuba. The goal was to get rid of Spanish influence in Cuba, as the ruler of the Spanish government had treated Cuban citizens unfairly.
Besides getting rid of the Spanish rule, this war would also help America gain access to new markets to sell their goods and new resources. Ultimately, this experience would help the US gain more power as the treaty that ended this war resulted in the US receiving territories like Guam and Puerto Rico.