I have a daughter like this. Part of it is that she is very bright, part is that she honestly enjoys arguing at first, before it gets frustrating for her, and part is that she wants to establish her place in the world. Unfortunately, she was this way with everyone, not just me.
The less talking, explaining, justifying and the like you do, the better! This was very hard for me, because I'm an explainer (sometimes an overexplainer), but I learned that the more I gave her a chance to argue, complain or justify, the worse it got. I had to give very short answers, including the old standby, "Because I said so." When she would attempt to turn around something she'd been told, as in your example, I'd say, "Excuse me, we both know that isn't what I said. I am not going to discuss this with you if you're going to behave this way." What she really wanted was my complete attention, so she'd attempt to start the argument up again. Two or three times I'd repeat that I was not going to discuss it, and if she persisted I sent her to her room.
Because she craved the attention, and the sense of dominating the conversation and me, this was more effective than anything else - explaining, clarifying or punishing. She hated it, and would say things like, "Oh, so now I'm not even allowed to talk?" I'd answer, "That's right. Not unless you're going to be polite." She'd attempt to bait me into arguing by saying things like, "You're not being polite!" but I'd refuse to discuss it, and send her to her room if need be.
She'd even try to start an argument in public by complaining to someone (in the store, at a relative's house) something like, "I'm not even allowed to watch TV, even though everybody else in the family does!" I'd respond, "That's right. That's because you were watching without your chores being done," and then I'd change the subject, refusing to go back and rehash or justify whatever it was. If she continued, I'd remind her that we were not going to discuss it further, and again send her out of the room if I had to.
I worried that her teenage years would be misery, but as she got older she actually got a bit better. She's 20 now, and often delightful, and learning to save her energy for things that really matter. Sometimes, she'll start reflexively arguing, but she's SO MUCH better now. This too will pass, as long as you refuse to feed the behavior. Hang in there!