The narrator likes cats and Montmorency does not.
When I meet a cat, I say, “Poor Pussy!” and stop down and tickle the side of its head; and the cat sticks up its tail in a rigid, cast-iron manner, arches its back, and wipes its nose up against my trousers; and all is gentleness and peace. When Montmorency meets a cat, the whole street knows about it; and there is enough bad language wasted in ten seconds to last an ordinarily respectable man all his life, with care.
Montmorency runs head long into chasing the cat as if it was his only mission in life. The cat, in this chapter, stares Montmorency down and he backs away.