When it comes to training an animal, there is no doubt that different limitations apply to different animals. Anyone who has seen a dog show will know that dogs can be trained to do a great number of things. Training a cat is certainly possible, but there is no doubt whatsoever that most of the training you can give a cat is corrective rather than creative. It is important to be aware of this before you set out to train your cat.
Undoubtedly, it would be fun if a cat could be trained to run around an obstacle course and bring its owner a rubber bone, like dogs can. However, this is never likely to happen because cats are not of that nature. You can train a cat to go in a litter tray, to stop scratching the curtains and to wait patiently for its food rather than try to catch it on its way out of the can. However, you will be waiting a long time to get it to play dead or roll over.
This is perhaps why people make the mistake of saying that cats cannot be trained. Without a doubt, you will not be able to convince a cat to do creative things, but this does not mean that it cannot be trained. You simply have to become conscious of the limitations. Sometimes, through practice, a cat will begin to do things that entertain, but this will be as a pleasant side-effect of a fuller training program. After all, cats like to play. Just give them a catnip mouse and watch them go.