First thing, never EVER argue in the slightest at that point. Because it is actually pleading, that's what it is. Very weak. It must not ever be about convincing someone, that doesn't work with a woman. It's like talking to the police if you are seriously suspected of something, or going to be charged - no, shut up! You are so tempted to argue the case then and there - don't do it. You will only get yourself in trouble, there is no upside. If she is genuine, then that's that, for the moment at least. You really need to change yourself at that point, but all these people saying you need to change to get her - well, that in itself is problematic. Why aren't you the man you want to be already? In which case, if you are, hell no, you are NOT going to change. So you can recover right off the bat by being good with it - cheerful actually. And walk away. But you have to not really mind. You kinda can't fake that. Best thing is to work on other women you are attracted to.
On the other hand if she is just playing some kind of game, testing and all that crap, being cheerful will end that nonsense very quickly. Keep having a great time, enjoy your life. LOL, wait till she gets a boyfriend than invite them both over to a party! Make the guy your friend! That will totally bowl her over. She will see that you didn't grovel. But... lol - you don't kinda don't want that kind of woman anyhow.
You do not want to be, never mind appear to be, the one who wants more out of a relationship than the other. To me, its easy, if she doesn't want a physical relationship to continue, then neither do I. People who constantly yo-yo all over the place with relationships sometimes have a chronic need for never-ending "relationship-dramatics". Why do you think people watch all these reality shows where people are all over the place with each other all the time?
Ever have someone who regularly says those dreaded words, " we need to talk about our relationship"?