So, I'm starting a little late this morning. I've been doing really good about getting them all done for 9 AM, but not today. I'll be back on time tomorrow, though!
Fighting and fights are a normal part of life and should be included in a story. Not necessarily all out brawls, but arguments, disagreements, spats, and bickering are good ways to add tension to a tale and depth to a character.
There are different kinds of fighting and who starts (instigates) and how each character involved behaves in the situation is great for making them real. When two characters are having an argument, depending on the topic, others around them may try to ignore it, or join in if they feel strongly about the topic. If three characters are having a disagreement about who should take possession of an item, someone may step in to be a referee of sorts. If five characters are having a physical fight, many others may rush in to help those they consider friends, or hold others back from trying to make it unfair, or ignore it all toghther. You may even end up with many spectators just watching as everything goes down.
Some people (or characters) are very nonconfrontational. They will do anything to avoid even the smallest dispute at any cost. Some have long fuses and will snap at odd moments for seemingly small things, while others with shorter fuses may blow up often. Some will manipulate any situation to their advantage to cause conflict--pushing buttons or playing both sides against the middle (kids have a tendancy to do this unintentionally, especially in situations where their parents have split up).
Something to consider is background. Certain heritages are famous/infamous for their ability to keep their cool or lose it. Its little things like those that can really add to a character, and it may give you some ideas as to what the character will look like.
Don't forget that everyone has a different fuse and different buttons that set them off. Someone that is typically a peaceful person, but is afraid of the dark would become more snippy in a situation where they would have to confront that fear.
The use of drugs and alcohol also need to come into consideration. When we use those substances, it changes our behavior and therefore, the way we react. Also, quitting a substance. Always try to find an interesting reason that someone is fighting.