¿Qué significa On the other hand, cats are proud "masters", while their owners are more like their "servants" ?

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Usually when somebody is talking about humans being like a cats servants they are comparing cats to other pets like dogs. You can train your dog to bring you things, you can train your dog to obey commands and some dogs are perceptive enough to understand the sound of crying or the change of breathing to mean you either want or need help. Most people don't train their cats to follow commands and they are often not sensitive to human needs or wants which makes owning a cat seem like everything you do is for them while they do nothing for you. Making you feel like you're their servent. If you call an untrained cat to come to you and they don't want to there's nothing that's going to convince that cat to come to you.
However it is a misconception that you cannot train your cat. If you start from an early age and use a reward system you can teach your cat tricks.