He was a soldier in the army before the infection. The reason why he went to the army is very simple: He felt alone and depressed, and he wanted to go to a place where he could make friends.
After he left the army he went to a vacation to Chernarus, but everything went bad. He met a man called Glenn Bankston. They tried to survive together but Glenn got robbed, and killed by bandits. Glenn had a son whose name is Glenn Jr. Bankston, and Matthew wants to find him to tell him this story and take revenge on those bandits.