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I tried convincing her but it seems that I keep failing at it.... ...
This is your first mistake. You can not "convince" her of anything. Trying to convince her of anything gives her all the power and makes you needy and gives her the perception you are of lower value. In other words you are giving her all the decision making power.
The bad news is she is going away and will be banging other guys in a week...if she's ugly, sooner if she's hot. OK that was an exaggeration and crude joke but the point is valid. She is going to have a world of opportunities and the REAL reason she isn't committing herself to you is she WANTS to have those opportunities and does NOT want to put limits on those opportunities.
That is her right and frankly at her age that is the right for her to do. I am siding with her on this one, let her go and let her go gracefully and with dignity.
HERE'S WHY-
Her leaving and getting other dicks stuck in her is inevitable at this point. it will happen whether you man-up and walk up with dignity and bang other chicks yourself, and it will happen whether you throw yourself at her feet and beg and snivvle like a little puppy.
The difference is if you walk away like a man and keep your balls attached and use them, she will see you as a sexual alpha and of higher value than a snivvling beta-boy.
If she see's you as an alpha she may still fuck you while she is home on breaks and chicks often bring girlfriends home on breaks and maybe you can fuck them too.
I suggest reading Roz's thread on break-ups from a woman's perspective. It is a little painfull to read but it's on the money in my opinion.
At your age when a girl dumps you, you think it is the end of the world and you'll never experience love or poontang again. But at my age (40s) I have seen A LOT of people fucking their X's months, years and even decades later. And whether they stand a chance down the road or not depends on how much of a man they were about the break up vs how much of begger and pleader they were during the break up.
The one's that walk away with dignity MIGHT get another chance at some point. The ones that beg and plead and cry NEVER do.