what are the main problems with moral subjectivism?

Ethical   Relativism
  is   a   meta-ethical   theory,   which   maintains   that   our   moral
judgments are essentially relative. Ethical relativism appears in two main versions, namely, Moral Subjectivism and  Cultural  Relativism.    Moral  Subjectivism asserts that  moral judgments  reflect  the  feelings  or  dispositions  of  an  individual  at  a  given  time.  Thus,  one’s moral   judgments   and   values   are   subjectively determined. Jean-Jacques   Rousseau defended  ethical  subjectivism  by  arguing  that  nature  is  superior  to  society.    According  to Rousseau,  an  individual  should  follow  his/hers  natural  inclinations  and  propensities,  i.e., natural virtues.  However, Moral Subjectivism has some very uncomfortable consequences:

1.  If  Moral  Subjectivism  is  correct,  then  two  individuals  may  have  different  moral judgments on the same situation and both of them may be right.  Thus, Subjectivism fails to explain what is right and wrong.

2.  If  Moral  Subjectivism  is  correct,  then  a  person  cannot  be  wrong  in  their  moral
judgments. If  my  moral  judgments  reflect  just  my  feelings  and  dispositions, then  I  cannot
be mistaken in my moral judgments.  After all, I am best familiar with my feelings.  Yet, I can  think  of  a  few  cases  in  which  I  have  been  wrong  in  my  judgments  because  of  my
feelings and emotions.  Thus, Subjectivism leads us to inconsistent judgments.

3.  Moral  Subjectivism  prevents  us  from  having  a  rational  discussion  on  ethical  issues.  When people are led by their feelings there is very little communication on ethical issues.

4.  Moral  Subjectivism  is  an  inconsistent  ethical  theory.    One  cannot  live  one’s  life  as  a moral  subjectivist.    Our  interactions  with  other  people  are  inevitable  and  require  some common understanding of what is right and what is wrong.
The  above  difficulties  ruin  the  appeal  of  Moral  Subjectivism  as  a  meta-ethical
theory.    There  is  a  fundamental  reason  for  the  failure  of  Moral  Subjectivism.    Moral Subjectivism ignores the fact that our lives are closely connected and our actions inevitably affect other people.  Ethics is the system of rules that hold our community together.  Thus, ethics is by its very nature inter-subjective.