The term 'bully breeds' was initially used to refer to all dogs that were bred for the purpose of 'bull baiting.' Bull baiting was a sport practiced in Great Britain in the 1700 and early 1800's. It was finally outlawed in 1835 when the Cruelty to Animals Act was passed by Parliament. This was a 'sport' in which dogs bred for this purpose were set upon a bull that was tied up or restrained. The objective was for the dog to sink it's teeth into the bull's snout and hold on. The English Bulldog was specifically bred for this purpose and excelled at the sport.
Given that it was a term primarily attached to the Bulldog, it later became a term to refer to a class of dogs that were 'bulldog' like. And from there it grew to include all brachycephalic (flat faced or pushed in faced) dogs.
Some people seem to believe that any breed that has the word 'bull' in its name belongs in this category. Though not true I prefer this misunderstanding to the one that assumes all bully breeds are bad and aggressive dogs!
Unfortunately, in recent times, people seem to have come to believe that the term 'bully breed' refers to dogs that they believe behave like the schoolyard bully. The truth is that there is not a single breed of dog that is inherently mean and aggressive. Though some can be trained to behave that way. And when that happens we need to blame the owners - not the dogs!
View this list of the breeds that are, in fact, included under the heading bully breeds. I really think you will be surprised at the variety of digs on this list!
You can question this list under any or all of these definitions of the term. The Pug and the French Bulldog, for example, were bred as companions, intended to be lap dogs. But they are brachycephalic breeds, so . . . Several of the breeds listed don't have the word 'bull' in their breed name. And though, unfortunately, several of these breeds were initially bred and developed for bull baiting and others for various forms of varmint hunting and fighting, they are no longer considered aggressive breeds and, in may cases, have come to be considered companion animals.
So I wish the term 'bully breed' would be dropped from the vocabulary of the general public since it is so easily misinterpreted. But if it must by used then I maintain that the term 'bully breed' should refer only to those breeds originally intended for bull baiting or are bulldog like in their appearance. This term should never be used and should not be used to define the behavior or personality of any breeds.