It's the one thing everyone wants to know from the very beginning: the truth. Who killed the comedian? What is interrupting Dr. Manhattan's view of the future? What mass destruction keeps being foreshadowed?
Later, he tries to go to the store to buy something for his mother. He encounters some bullies who start making fun on him and his mom, calling her a whore and him diseased. To punish the tormentors for such disgusting insults, he attacks them. He feels he needs to defend the reputation and dignity of his mother, even though she shows no signs of protecting him throughout the novel.
Learning about Rorschach's childhood helped me understand his ruthlessness and violence as an adult. But I also started to wonder if this character was so crazy about justice that he was blind to the injustices in his own behavior. Partially blinding a child is too harsh of a punishment for the crime of heckling and harassment. But Rorschach almost seemed proud of his work. He doesn't care if societies morals and thoughts of him are skewed. He sticks to what he believes in. I couldn't help but wonder if this kind of savage punishment and brutality would help promote peace, or tear it apart.