If we ask about the reasons for believe in a universal moral grammar the only answer that can be offered is a descriptive one. Study of diverse moral cultures reveals this grammar. These get translated into the interests to direct behavior which are the moral systems humans create.
All moral cultures are concerned to control lying and deception.
They all interpret intentions based on behavior when language is unavailable. They conceive of each as responsible to the others. They distinguish voluntary and involuntary behavior, diminish blame on the grounds of accident, mistake and ignorance of consequences. They value empathy. They evaluate behaviors by using both moral rules and role relationships, thereby regulating sexual access, exchange of labor, goods, and services.