We don't define galaxies in general to spin in the opposite direction.
Just the Milky Way.
(The reason for this seems to be that Galactic "North" was defined long before we had the data to determine which way the Milky Way rotated -- or even that it rotated. By the time the rotation was definitively determined, it was too late to override convention. This may go back to William Herschel deciding that the "north pole" of the Galaxy should be in the same hemisphere of the sky that the Earth's north pole pointed toward. In retrospect, he had a 50% chance of being right...)
Just the Milky Way.
(The reason for this seems to be that Galactic "North" was defined long before we had the data to determine which way the Milky Way rotated -- or even that it rotated. By the time the rotation was definitively determined, it was too late to override convention. This may go back to William Herschel deciding that the "north pole" of the Galaxy should be in the same hemisphere of the sky that the Earth's north pole pointed toward. In retrospect, he had a 50% chance of being right...)