Harris is…well, he's not Birdy's favorite. Sure, they're in the same unit, but Harris is kind of the opposite of Birdy. In the beginning, Birdy's nervous about whether they'll be ordered into Iraq, while Harris is rearing to go. He can't wait to see action.
And he doesn't really change.
Throughout the book, Harris is all excitement and bravado, posing with his gun and a sandstorm in the background, going on and on about his time in the Gulf War, throwing a punch at Jonesy when Jonesy calls him out for disrespecting women.
Could it be that Harris is just trying to show off for the gang? Earlier in the book, before he and Jonesy fight, he yells "Jonesy, check this out!" (4.27) when he poses with the bayonet on the end of his weapon. Then Jonesy, Marla, and Birdy get close—with Harris on the outskirts. Maybe he's a little salty about it.
Or maybe he's just a jerk.