I was looking through Siamese Rescue before I finally brought Yin Yin home (I still do now and then to see who found a home and so on) and one very intelligent Siamese kitty was "returned" (as if she was merchandise, sigh!) because she attacked the owner's "birdies". This person had assumed the cat and birds would be fine together. Of course not. Birds are prey for cats no matter the breed!!
There are occasional cute stories about birds and cats who do well together but those are rare circumstances that have taken months and years of training. (and even then I bet their humans do not leave them alone together!)