Bballjones and markji are both correct. There could be a million reasons. There are some women that get pissy and will argue with you, but something ELSE is bothering them, and they wont tell you until later. Sometimes you have to either show them you care by saying how you really want to know what's bothering her and convince her to tell you (While swallowing your pride) or you have to be patient and let her display her true feelings when she is ready.
Or she could be an illogical crazy son of a biscuit, as bballjones said. Whether you're attracted to that is up to you. Personally, I stay away from them. In fact, I was just on and off dating and talking to a girl just like that and am happy that's over.
Or she could be like not just some chicks, but some guys too, and make illogical arguements, just for the sake of argueing or hearing themselves speak, or maybe she really thinks she's right, even though completely illogical. You don't think some guys are like this? Check out this message board on a website called ultimateknicks. There are a couple of people like that. 
Or maybe she's just confrontational. Either way, it's up to you to figure out what it is. Maybe if you tell us the story (Which you don't have to if it's private obviously) we can maybe help you pinpoint it better.
A million possibilities, a million solutions!
Good luck broham.
“Whenever I’m about to do something, I think ‘Would an idiot do that?’ and if they would, I do NOT do that thing.”- Dwight Schrute