When a new pet is introduced into a household there is a natural recipe for fighting. Sometimes this can take the form of a cat becoming aggressive towards a dog!
There are two basic instincts that apply when pets are mixed in a family environment:
1. Establishment of a "pecking order" - in other words which individuals are higher than others in the "pack" or "family". Pack dominance is more typical of dog behaviour than cat behaviour, but of course cats are highly independent and will defend themselves if another animal tries to dominate them.
2. Cats like to establish and dominate their geographical territory. Once they have decided the borders to their territory cats will naturally want to dominate all other animals found within those borders - including dogs if they happen to share the family home. When a new cat is introduced into a home that already has a cat they will often fight a lot - and actually may both believe that they dominate the territory - resulting in a permanent tolerance but dislike for each other with sporadic bouts of fighting.
Fighting at other times may be due to changing circumstances - such as a female becoming aggressive when nursing a litter of puppies/kittens.
Unfortunately aggression between species is more difficult to treat because they are being aggressive to each other for different instinctive reasons.