In a society should each person determine for himself what is good and bad or what is right or wrong? How is a standard to be determined for everyone since we all don't agree?

Good and bad are subjective terms depending on what culture is defining those terms.  For instance, one culture will elevate mass murder to an act of worship, while another will decry such an act as the epitome of evil.  Some cultures will say treating women and homosexuals as equals is beneficial to society while others will say it is detrimental.  Mankind has always been at war with itself over the definitions of good and bad, and most likely always will.  I will fight to defend my definition of those terms until convinced that my understanding of good and bad is in need of an adjustment -- as has been the case a number of times during my life.