One great storyline could be them teaming up to fight a common enemy like a powerful meta - human who is causing chaos in both of their cities. They could start off not trusting each other fully due to their different methods but then grow to respect one another as they see the value in each other's skills.
Supergirl is very much about truth and justice in a big - picture way. Green Arrow focuses on the justice that needs to be served on the streets. Their personalities could clash when they first meet as they might not understand each other's motives fully. However, as the story progresses, they can start to see how their different views on justice can work together. Supergirl can use her powers to help Green Arrow with larger threats that he couldn't handle alone, and Green Arrow can show Supergirl the importance of the little things in protecting a city.
Love and romance can be a theme in some cases, not necessarily between Arrow and Supergirl directly, but perhaps within their respective teams or with other characters they interact with in the fanfiction world. It adds an extra layer of complexity to the relationships and the overall story.
In Arrow and Supergirl fanfics, the theme of friendship or romance can also be common. Some writers like to explore the possibility of a romantic relationship between them, while others focus on a strong platonic friendship. Additionally, the theme of facing a greater threat together is quite prevalent. This could be an alien invasion or a super - villain that is too powerful for either of them alone. Fanfics use these themes to create exciting and engaging stories.
Green Arrow isn't typically portrayed as an asshole. He's often a hero with a strong sense of justice, but like any character, he has his flaws and moments of difficult choices.
Yes, it can be. It often gives enough background within the story so that new readers can follow along. They'll quickly get a sense of who Green Arrow is and what he stands for.