Personally, to me being in debt isn't necessarily a bad thing. It can help build credit by proving that you're financially responsible. Especially when you don't have much of a credit history.
In the end it's a very personal choice. Investing in an S&P index fund or the like will get you around 10% return per year on average but it has some risk. Paying off the loan has no risk, you basically save the interest payments over the life of the loan. BUT, paying off the loan has no upside either. The S&P index fund could give you more than a 10% return if your timing is right (or lucky).
There's no reason that you couldn't do a little of both. Throw some extra money at the student loans each month and throw some money into some investments.
Now, if you're gonna throw in other real life factors like car loans, credit card debt, and the like, that's a different story. Typical car loans have higher interest rates than student loans and credit card rates are usually about twice that. So, I'd put paying off credit card debt at #1, throwing a little extra money at your car payment at #2 (while also throwing a little into investments), and upping the student loan payment a bit at #3 (also while investing a bit at the same time).
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Strive to be more curious than ignorant.
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