Why do I owe money instead of receiving money after filing my taxes?

No one claims anybody as 'independent'. If your parents are still claiming you as a dependent, that means your standard deduction is much lower than if you were claiming yourself. In that case, it would be $12,200. You would not begin to owe any federal tax until you earn more than that. If your parents may still claim you, your standard deduction is limited to $1,100 and you begin to owe federal tax above that amount.

,You didn't prepay enough.

You didn't have enough withheld to cover your tax obligation. My guess is that it has to do with how yo set your W4

Gee, did you make more money?  The standard deduction is no more than $12,200.  Note a dependent's standard deduction ranges from $1100 to $12,200, using a formula of earned income PLUS $350.  (See IRS publication 501, page 25.)  If all you had was earning from a W-2, you wouldn't owe tax until you made more than $12,200.

Tell us what was in boxes 1 and 2 on your W-2.

You didn't correctly fill out your W-4 form to have the correct amount of taxes withheld from your paychecks.

When you have too much money withheld from each paycheck - you get a refund of that over payment.

When you don't have enough money withheld from your paycheck - you owe more.

File a new W-4 form with your employer to try to correct any errors to have a little more withheld from each paycheck.

If your parents will not claim you as a dependent on next year's tax return, then your situation might improve without making any changes.  If you will still be their dependent for next year, then you need to be sure to change your W-4 form.  

You have ALWAYS ahd to pay. What changed is in previous years, they withheld too much during the year and it exceeded your tax liability. Recent adjustments to the withholding tables resulted in keeping more of each paycheck, instead of getting it back when you file your return. In reality, you are the only one that did it RIGHT.

Most likely they were withholding too much at your previous job and too little at your current job. The ideal situation is to have the right amount withheld (from your W4) and not owe any money or get any money.

Impossible to say without seeing your tax return.