Casting of objects - trying to turn a dog into a cat ... why?

After Craig's lesson on type casting objects and upcasting and downcasting, I read up further on the topic as I was a bit confused with it all. On the community forum I came across a link that explains the concept of upcasting/downcasting and there the author mentions that you can 'turn' one type of object into another that is, to some extent, different.

The author gives an example towards the end where he creates two different classes; Cat class and a Dog class, and mentions that he can make a dog out of a cat - using the properties form the dog class.

I understand the process, I think, but I'm confused why one would do such a thing? It seems to me quite convoluted and verbose. I suppose we could argue that there are certain properties both cats and dogs share (4 legs, teeth, two eyes, fur, tail, etc), but why complicate things? Why not just keep the specific properties within their allocated class objects, even if we have to repeat some of them? I think this would make the instances of the objects clean and clear when called.

I know I mentioned a taboo amongst programmers with the 'repetition', but I feel that certain things are okay to repeat for clarity within code ... or am I being too much of a newbie?

Please, any input or personal experience would be highly appreciated.

Here is the link to the example on upcasting/downcasting I read. http://www.cs.utexas.edu/~cannata/cs345/Class%20Notes/14%20Java%20Upcasting%20Downcasting.htm

Thanks Gábor