In the 1920's motorcycle racing was an extremely popular sport in the US. All the major manufacturers saw the advertising potential of winning a big race in front of a crowd of thousands, and so all the major manufacturers had their own sponsered teams.
One of the racers in the Harley team had a pet pig, which he would ride around the track with, if he won, as a lap of honour. All the other Harley boys also started doing it, and soon they became known as the 'hogboys'. From there it was a simple step to make what they rode the 'hogs'.
During the biker 'trouble' of the 50's Harley-Davidson didn't like the name 'hog' and tried to stop people using it in reference to their motorcycles. A few decades later, after bad times and good, including the company going through a management buyout, they changed their tune, and started sending in lawyers to stop people using the word 'hog' in any motorcycle business, that was not associated with theirs.
After some dodgy court cases, it turns out that any large motorcycle can be a 'hog'.