Should I pay off my student loans?
From a financial-only standpoint your reasoning is sound. But your girlfriend is probably just fiscally conservative/anti-debt by nature. So am I. The main question is this: what are you doing with the extra 2% + tax savings you are "pocketing"? If you are simply spending it on consumables then it doesn't really have any positive financial impact whatsoever for you in the long term and you would be better off paying off your loans. But if you have enough self control to save that much each month then you are benefiting from it.
This is a moot point. Does not matter what he is doing with the interest, it's a net gain regardless. I am extremely fiscally conservative (ask my wife), but if it simply DOES NOT make sense to pay off a loan with such low interest rate. The fact that he has such a high interest bearing savings account only strengthens the case.
It does not make sense to pay it off even if he did not have the interest bearing savings account, unless he has no intention of borrowing ANY money for the remaining period of the amortization schedule, which is highly unlikely. Looking at his age, it'd be a safe assumption that he will purchase a home or finance a car before the payments are up. In which case, his monies would be much better served as a down payment on a 5-8% loan.
Further, having the liquidity is a much better option than getting rid of a loan with >1% interest. I have had the cash needed to pay off all of my student loans (a considerable sum) for more than a year. Unfortunately I was laid off in July. Had I used those monies to pay off my student loans I'd be in a much less tenable position at the moment. That liquidity has saved me a lot of peace of mind.
Plain and simple, it makes absolutely no sense to pay off such a low interest loan ahead of schedule. It is making you money (due to the interest bearing account). It gives you the opportunity to put those monies to greater financial use. And it gives you flexibility if hardship arises. The only reason to pay it off is "so you have no debt", which is an antiquated, old school thought process. There is absolutely no logical reason to pay it off now.