Humans are social creatures. We have a need to involve others in our lives, to spread ideas and work with our fellow man. Sometimes this social requirement works in our favour – we worked together to get to the moon, and we invented pie! But occasionally our need for social interaction means we come across someone that we wish would just... catch on fire.
There is sometimes a logical origin to a feud. When two people of differing beliefs are in a similar position, it's entirely understandable that they may butt heads. This tends to be why organised sports produces the best rivalries, each side wants to win and by winning can prove their superiority. Outside of sports, though, people have found some ridiculous reasons to battle, both physically and mentally.
Many of the following entries need a lot of historical context to truly understand why these people fought, and unfortunately this context is sometimes lost within the fog of time or hearsay. It's difficult to say who was right and who was wrong - this is subjective - but what is fair to say is that the inevitable feud that followed, although predicated on logic, became something far more venomous as time went on.
There are two sides to every argument and it's up to the judge to decide who wins; in this context, you are the judge.