Anecdote: “My cat plays with its right paw”
Individual or Activity-Specific Cases: “Horses reliably pick one leg to lead their galloping” or “Chimps prefer to fish with their left hand”
Marginal asymmetry: “X chimps are right-handed for every Y left-handed chimps.” [where X/Y < 9] Let's be clear: handedness in humans is immensely asymmetric (9:1) at the population level, and holds across multiple tasks within individuals (most people are right-handed not just for writing, but for throwing, batting, fishing, etc). So while anecdotes are entertaining, activity-specific cases are interesting, and marginal asymmetries are common (after all, motor programs such as galloping usually become automatized and require that some leg be used first), none of these traits alone can be used to demonstrate handedness as it exists in humans, since humans manifest all these traits in combination.
Why shouldn’t non-human animals have handedness to the extent humans do? Corballis argues it has to do with the development of language – but that’s the previous post.