Why do I owe New Jersey taxes and I live in Philadelphia

[DMarkM1]

You likely do not, however NJ is probably showing on one of your income forms indicating you worked in NJ, taxes were withheld, and you have not removed those wages from NJ taxation.  

NJ and PA have a tax reciprocity agreement.  That agreement states only the resident state will tax your wages/salary.  So if your employer mistakenly withheld NJ taxes (showing in W2 boxes 15-17), then on your non-resident NJ return you need to allocate zero "0" wages to NJ. This will result in the taxes withheld being refunded by NJ.

If not enough taxes were withheld for PA you will owe taxes there as your resident state taxes income no matter where it is earned.  

If you haven't already you need to have you employer stop withholding for NJ and have PA taxes withheld instead per the reciprocity agreement.  

[TomD8]

File NJ Form N-165 with your employer in order to stop the NJ withholding.  Here's a link to the form:

https://www.nj.gov/treasury/taxation/pdf/current/nj165.pdf