It means that you are being blown over too easily. Cats are known for being relatively cuddly and cute creatures. Their main goal may be to kill or to hurt you like a lion does, but since these cats usually weight under 30 pounds, a cat attack directly to your face should in theory just be soft and cuddly. You may get a bruise or a serious cut from it, but if push came to shove, in a cat attack, you should be able to overpower the animal almost immediately.
Therefore if you are beaten by the cat and it is able to take you to the ground and destroy you or put you down then this means that you have been letting yourself get too easily pushed over by simple problems. Maybe this means that you have an issue to solve that would be theoretically simple and you are making it a lot more complicated than it has to be. Maybe there is a fight that you know you can win, but for some other reasons you are letting your opponent best you. A dream like this should be a warning to you that you need to go out there and try a little harder if you hope to preserve your honor. You really need to try your hardest to make sure that you overcome all of the problems that you know it is possible for you to overcome or you will get nowhere in life.
To dream that you are in the midst of a cat attack and you are the one winning could mean that you need to tone down your aggression. After all, a grown man or woman should not be “winning” a cat fight. The worst that you should do to a creature that is that much smaller than you is to remove them from you even if they have harmed you. The fact is you are in a remarkable position of power that should allow you to easily overcome a cat, and to use this power to its fullest extent could kill it. As humans we possess an intellect which allows us to realize that we are causing other creatures pain and doing moral wrong. Thus, if you are harming cats in your dream, even if they are the ones that started the fight, it still means that you need to calm down overall and tone down your aggression in real life.
You have probably gone through something serious which has caused your perspective in the world to become a little bit more negative and is causing you to feel great displeasure. Don’t allow yourself to take it out on a group of innocent people.
One last thing to consider though is that cats are not known for being aggressive unless you’re thinking of a giant cat like a lion. Most cats are fairly peaceful and would have to be goaded into fighting unless there were some kind of other circumstances that you were not aware of. Don’t worry too much about the cats, just worry about how much you worry. Try to calm down a bit, because if you’re that worried about cats attacking you that you are having nightmares about it, then your vision is not very realistic.