When you file a grievance, the grievance becomes the property of the Union. The Union representatives and officers alone make the determination whether the grievance has the merit to advance from one step to the next including taking it to Panel or Arbitration. You do not have the right to force your Union to arbitrate a grievance. You DO, however, have the right to file a DFR (Duty of Fair Representation) charge against your representative with the NLRB and have them investigate the Unions actions and reasons for not pursuing your case.
Now, as a Business Agent, I can tell you that if your rep decided not take a case to arbitration, there is most likely a VERY good reason for it. I have done the exact same thing. I informed the member that my decision was final, and if they did not agree with it they should file a DFR (Duty of Fair Representation) charge with the NLRB. They did exactly that, and the NLRB decided against the members claim.