Using "I am" and "you are" implies that the subjects ("I" and "you") actually ARE a cat and a dog, whereas using "I were" and "you would be" implies conditionality (that is, "IF i were a cat, THEN you'd be a dog (but we may not actually be a cat and dog)"). Grammatically, this has to do with what's called the "subjunctive mood". The difference is subtle, though. I think using "I am" and "you are" gets the point across, and should be accepted as well.
I still think "I am / you are" should be accepted. When I read the sentence, the scene I imagie is two children playing. One yells "I'm a lion and you are a cat! Raw!" The other replies "No, then we can't play together. Lions are in a zoo and cats are in the streets! If I'm a cat then you are a dog!". In their game of make-belief they actually are a cat & a dog.
Calling someone a dog in most languages and cultures (Western, Eastern, and everything in between) is considered an insult due to a dog's ability to take commands from humans and their incredible sense of smell, which can both be used for "evil" purposes. Tracking people with dogs was considered an early form of privacy invasion by some, especially Muslims since they were used to track the Prophet Muhammad and he forbid Muslims from taking advantage of a dog's sense of smell for "evil" purposes. It's a common misconception for Muslims to think of dogs as "evil" or "vile" creatures, but they were actually spoken highly of in the Quran in the story of the Seven Sleepers, a well as a hadith speaking of a woman helping a dog, and it was only abusing their "powers" the Prophet Muhammad had a problem with. Since Indonesia is the world's largest Muslim-majority country, it makes sense for them to have strong views towards dogs in those respects. It would seem being man's best friend comes with a bad rap.
Well I don't know if that is a reason in Indonesian, in Morocco people know the hadith in which the Prophet taught the muslims how to use a hunting dog, so there is no problem in 'using its powers'. What they do have a problem with, is that the Prophet taught them that the saliva of a dog is impure (so you need to wash it off before praying), looking at what science found about the bacteria in dogs saliva, I can only agree. The reason why many muslim people look down on dogs is not because of the Prophet (who used to allow a stray dog to enter his home to feed it), but because they are mostly farmers or city dwellers children of farmers. Everywhere in the world, whether muslim or not, Arab, Spanish, Argentinian, you'll see that farmers see the dog as the lowest of all farm animals.