what was the reasons behind gods and goddesses rivalry

Based on prior history, the gods and goddesses favored one side or the other.  For example, Athena and Hera were angry at Troy because Paris awarded the golden apple labeled "For the Fairest" to the goddess Aphrodite.  She, therefore, favored Troy.  Achilles' mother got a favor from Zeus when she was allowed to dip Achilles in the river which would create immortality; he was granted that from all wounds except on his heel where his mother held on to him while dipping him.  In general, the gods favored one side or the other for petty reasons, most of which seem very human in their actions and motivations.