Crows are very aggressive birds. They will go after just about any other bird, especially as a flock. I have seen them go after Great Blue Herons, Egrets, Turkey Vultures, and this Peregrine Falcon.
One reason for the crow's aggressiveness is protection of their young, true of most wildlife. When crow babies are fledging and leaving the nest, and can't fly well. So they are vulnerable to predation. They hide in the trees and the parents are very protective of them. They will attack potential predators. But I have seen them individually go after other birds throughout the year.