Character Analysis
We can ask of Orestes the same basic question we asked of Electra: why does he want to kill the royal couple? Unlike his sister, Orestes is driven in large part by the command of the god, Apollo. In the first scene, he even ignores his sister's cries of woe because he's so concerned with doing what Apollo told him to do. If he acts out of duty, it looks as though he is more concerned with honoring the gods than honoring his father.
Like Electra, Orestes is so consumed with the task at hand that it's essentially come to define his life. His whole existence has been about his growing up just so that he could come back to Mycenae and get rid of the couple who killed his dad. This task has become his identity. We are hardly surprised, then, that Orestes is so single-minded in his action. He's not messing around either: his life has been building towards this moment since he was smuggled out of the palace as a baby.
One of the issues we might take with Orestes is his failure to inform Electra of his fake-death plan. He lets his poor sister wallow in nearly suicidal misery under the misconception that her brother, her only savior, is dead. So in fact, we need to understand the motivation behind Orestes's single-mindedness, so that we don't condemn him for what seems like an oversight. He wasn't deliberately trying to make his sister suffer; it's just that consoling her was not part of the plan. He came to Mycenae for one reason and one reason only, and he's certainly not going to get sidetracked on his way.