She eats chicken but not fish?
Also, "she is eating chicken but's not fish" is not correct English.
´She eats chicken but not fish´ is correct English if you are talking in general about someone´s diet.
So you mean shes saying she's not eating chicken and fish at the same time?
With this sentence it is in general, ie what she usually does- she eats chicken but doesn't eat fish (because she doesn't like fish, for example).