How did president mckinley justify the u. s. takeover of the philippines

President McKinley didn't have to explain anything, the US did not "take over" the Philippines.

The Philippines were under Spanish Imperial colonization.
It was no different than Cuba or Puerto Rico, just another Spanish colony they had taken over the years.

Revolts against Spanish rule had been endemic for decades in Cuba and were closely watched by Americans.
The Americans weren't too fond of Cuba, but had actually offered to purchase Puerto Rico from the Spanish, in which the Puerto Ricas were quite pleased about, rather being under US govern instead of the long term neglect of Spain.
Spain declined.

The nickname would be : " robber bandits" i believe