Bull-baiting was a popular blood sport in England where dogs, usually bulldogs, were pitted against bulls. These dogs were specifically bred for their strength, tenacity, and ability to hang onto a bull's nose, despite the bull's much larger size.
Therefore, the name "bulldog" reflects their original purpose, not their size relative to bulls. While modern bulldogs are smaller than bulls, the name remains a testament to their historical use in bull-baiting.