Neither of you are exactly right (if you've interpreted your friend's theory correctly).

Depending on the number of allowances you claim, a portion of your paycheck will be withheld each period for taxes.

When you file, your total income, exemptions, and deductions will be used to determine how much tax you actually owe for the year. The total amount withheld will be subtracted from that amount, and the net difference will be either what you have to pay when you file (if you didn't withhold enough) or what refund you get (if you withheld more than what you owe).

So it's not technically true that you'd pay back whatever you withheld, but I suspect that's just a bad interpretation of what your friend told you.

Then would it be better to pay more taxes when possible because then I would be receiving more tax refund?

Sure, if you don't mind loaning the Treasury your money interest-free. It's actually not a terrible savings plan for those that don't have strong budgeting discipline. A smarter plan would be to withhold as close to the amount of tax you will owe as possible, so you have neither a large tax bill (which messes up your cash flow and risks underpayment penalties) or a large refund (which is an interest-free loan to the Treasury).

Neither of you are exactly right (if you've interpreted your friend's theory correctly).

Depending on the number of allowances you claim, a portion of your paycheck will be withheld each period for taxes.

When you file, your total income, exemptions, and deductions will be used to determine how much tax you actually owe for the year. The total amount withheld will be subtracted from that amount, and the net difference will be either what you have to pay when you file (if you didn't withhold enough) or what refund you get (if you withheld more than what you owe).

So it's not technically true that you'd pay back whatever you withheld, but I suspect that's just a bad interpretation of what your friend told you.

Then would it be better to pay more taxes when possible because then I would be receiving more tax refund?

Sure, if you don't mind loaning the Treasury your money interest-free. It's actually not a terrible savings plan for those that don't have strong budgeting discipline. A smarter plan would be to withhold as close to the amount of tax you will owe as possible, so you have neither a large tax bill (which messes up your cash flow and risks underpayment penalties) nor a large refund (which is an interest-free loan to the Treasury).