As wonderful as dogs are, most dogs will exhibit some sort of aggression at one time or another in their life. For the bullmastiff, animal aggression is a problem that has many owners running straight to their local dog trainers.
Dog aggression may not sound that serious to some people. They believe if their bullmastiff is the only dog they own, they will probably never encounter another dog, so there shouldn't ever be any reason to be concerned. The fact is that most dogs encounter other dogs at the park or in the neighborhood. Many families own more than one dog. Not to mention the fact that the bullmastiff doesn't just suffer from dog aggression, but animal aggression. Chances are he will encounter other animals, which can create a real problem.
Bullmastiffs don't always get along well with other dogs. In particular, males don't seem to like dogs of the same sex, regardless of the breed of the other dog. Occasionally, female bullmastiffs have been known to fight with other females as well. This may all stem from a dominance issue, where they are both fighting to become the alpha. Regardless of the reason, considering the large size of the bullmastiff this can be a very serious problem if not corrected immediately.
Many feel that the guarding instinct the bullmastiff is born with contributes to much of their animal aggression. This may play a part in it, but training should still be provided for the dog at as young an age as possible. It is also important that they be socialized around other animals at a young age.
I have two German shepherds that I have raised from birth. As soon as they were both old enough to train I took them with me on road trips to friends' houses that I knew had either cats or dogs. I believe it's easier to cure dog aggression than aggression towards cats, but that may be a personal opinion based on my own experiences. Bullmastiffs, largely because of their massive size, like to dominate smaller animals and very seldom will you find an animal that is not smaller than they are.