Why do i owe federal taxes if i claim 0 have no dependent?

There are many reasons why you might owe this year, such as: 

• You income increased.
• You did not qualified for the full amount of the Child Tax Credit. 
• You changed your Filing Status.
• You didn't qualify for the Earned Income credit. When you qualify, the credit amount will go up as you earn more income, but once you earn too much, it will go down eventually to zero. TurboTax will figure out exactly how much you’ll receive. 

Review your entries to make sure you entered any federal taxes withheld on your W-2.

Without looking at your return it would be hard to know why you owe federal taxes. I would recommend that you make a line by line review with last year's return.