I think it depends on the boxer. Our Calli (pit/boxer mix) never chased our cats. When we got Calli as a puppy she thought she was one of the cats, our biggest cat actually held her down and bathed her. Our second boxer Berk was interested in our cats but never really chased them much however when we got our third boxer Teaki it was a different story. Teak and Berk loved to chase the cats and corner them. It seemed like they actually thought it out because one would go one way and cut the cat off while the other one chased it into a corner. Our 4th boxer Zig just likes to play with them like they are another boxer.