Why does Stargirl go against social norms?

The simplest answer to this question is that Stargirl goes against social norms because that's just who she is. Digging a little deeper, readers see that Stargirl goes against social norms because she loves everybody equally and unconditionally. It's why she is able to not only avoid retaliating after Hillari slaps her, but actually kiss her. Stargirl genuinely wants to make the lives of other people better. It's why she cheers for both teams. It's why she reads the newspaper and pays special attention to things like death notices, birthdays, and wedding announcements.

What she read were the parts that most people ignored, the parts without headlines and pictures, the boondocks of the paper: the hospital admissions, the death notices, the birthday and wedding announcements, the police blotter, the coming events calendar.

She loves to use this information in order to do her random acts of kindness. Stargirl is innately altruistic, and she acts on those feelings and impulses. It's a strong commentary on people and society that they view her as being so odd. Societal norms tell people to be selfish. Many people say they help themselves in order to help others, but Stargirl flips that around. She helps others in order to help herself.