The title is a play on the children's game "Follow the Leader".
The swallows are returning to the Mission of San Juan Capistrano. A hungry cat is watching them on radar. When the first bird nears, the cat disguises his mouth as a nest. However the swallow notices the cat's teeth and drops a jack-in-the-box in the nest, then watches as the cat's neck springs up and down. Then it paints a metal bird ornament to look just like itself. The cat greedily swallows the ornament, then the swallow uses a magnet to pull the cat around the yard, through the fountain, bumping up every rung of the ladder, across the clay tile roof, down to the ground, then up and down a flagpole a few times. The cat straps boards to his arms and tries to fly, but the swallow turns on an electric fan and blows him off the roof. The cat climbs the ladder and fires a shotgun at the bird, but the recoil propels him and the ladder backwards. The cat dons a Superman costume, but the bird hooks a spring between him and the well so when the cat leaps, he is pulled back into the drink. He finally catches the bird with some flypaper, but just then the rest of the swallows arrive. They swoop at him, drop tacks in his path, pelt him with light bulbs, and pick him up and carry him to the town line. He vows that he's not leaving town without a swallow, and he finally gets one... from the bar across the street.