If I got charged with a felony and I was granted youthful offender status, why would an employer be able to pull it up on a background check?

Different states handle convictions by persons under the age of 21 differently. Most states will allow a youth to be convicted under a special statue that allows a criminal case to remained sealed from the public so long as all court ordered conditions are met. You will want to either contact the court in which you were sentenced or your attorney to determine if your conviction has been sealed from the public.