His connection with Gotham City. Batman has a deep and personal connection with Gotham, and the city almost seems to be an extension of him. In fanfiction, Wonder Woman, who is more associated with Themyscira, might envy this strong bond. She may feel that his relationship with Gotham gives him a unique identity that she lacks in relation to any particular place.
There are several potential reasons. Catwoman's agility and stealth skills might be a source of envy for Wonder Woman. While Wonder Woman is strong and powerful, Catwoman's ability to slink around unseen and steal things right from under people's noses is quite impressive. In addition, Catwoman's relationships with other characters, especially those in Gotham, might be more complex and nuanced than Wonder Woman's relationships in her own world. This complexity could lead Wonder Woman to feel jealous in fanfiction, as she may long for more interesting and less straightforward relationships herself.
She may not like the false interpretations of Batman in some fanfictions. Fanwriters might change his personality or motives, and as a fellow hero, she doesn't appreciate that.
It could also be due to mind control. A powerful villain might have controlled Wonder Woman's mind and made her turn against Batman. In this scenario, Wonder Woman would act against her own will and kill Batman, creating a tragic situation in the fanfiction.
Yes, there are quite a few. In some fanfictions, Wonder Woman might be jealous of Batman's popularity among the public or his close relationships with other heroes. For example, she could be envious of how Batman seems to have a special bond with Superman in some storylines. This jealousy can add an interesting layer of drama to the stories.
One possible reason could be their different approaches to justice. Batman is more about vengeance and using his own set of rules in Gotham, while Wonder Woman comes from a place of more idealistic and Amazonian values of justice. Their clash in ideologies might lead to an argument.
One reason could be a misunderstanding. Maybe Batman suspects Wonder Woman of being involved in something she's not, like a potential threat to Gotham that he misinterprets. Another could be ideological differences. Batman is very much about justice in his own city, while Wonder Woman has a more global and myth - inspired view of justice.
One idea could be that Batman and Wonder Woman are both vying for the attention of a new superhero in town. Batman is jealous because Wonder Woman seems to have a natural connection with this new hero, perhaps due to their similar powers or backgrounds. Wonder Woman, on the other hand, is jealous of Batman's detective skills which the new hero seems to admire a great deal. This could lead to a series of challenges and competitions between Batman and Wonder Woman to prove who is more worthy of the new hero's friendship or alliance.
To realistically portray their jealousy, it could be related to their insecurities. Batman might be jealous of Wonder Woman's god - like status and the respect she gets from others because deep down he feels inadequate without his gadgets. Wonder Woman could be jealous of Batman's strategic mind and the way he's able to solve complex problems so quickly. This jealousy could manifest in how they interact with the other Justice League members. For instance, Batman might be overly critical of Wonder Woman's decisions in front of the others, and Wonder Woman might undermine Batman's authority subtly. It's all about showing the human (or superhuman) emotions beneath the capes and tiaras.
Batman might avoid Wonder Woman in fanfic because he's afraid of getting too close to someone with such strong emotions. He's used to suppressing his own feelings, and Wonder Woman is very passionate. Her presence could stir up emotions in him that he doesn't want to deal with in the fictional stories.
In the fanfiction, perhaps Wonder Woman is trapped in some sort of magical or technological prison created by an enemy. Batman, with his detective skills, figures out how to break in and free her. He might have to solve a series of puzzles or overcome various security measures. He then rescues her and they team up to take on the bad guy who imprisoned her.