Explain the reasoning behind ismene's decision not to antigone bury polyneices and what it reveals about the ancient greek culture.

Two types of loyalty were displayed in Antigone. One was to family and the gods, the other to Creon and his mortal law. Ismene's choice to not help Antigone was based on her fear of Creon, since she stated that she fears the consequence of disobeying Creon. This decision displays the family divide, Antigone's characteristics of being headstrong and stubborn, as well as a theme of why you should not cross the gods.
In terms of Ancient Greek culture, the women in the family were the ones who prepared the body and held a "funeral". Antigone, living up to this culture, took upon the female role and did her duty of burying Polyneikes. This ties in with Ismene, as she is defying, in a sense, Greek culture as it is the gods you are loyal to. 

Summary: Ismene is fearful of the consequences, and defies a woman's role in preparing the body for burial.