The number of Robins in Batman comics varies depending on different storylines and continuities. Generally, you can count at least four significant Robins: Dick Grayson, who was the first; Jason Todd, who had a more tumultuous story; Tim Drake, known for his detective skills; and Damian Wayne, Batman's son.
It would be a very dark and twisted take on the Batman story. The whole dynamic between Batman and Robin would be completely changed. Robin would likely be filled with rage and a desire for revenge against Batman. It would also shatter the image of Batman as a hero in the traditional sense.
There may or may not be such a 'batman kills robins parents fanfic'. Fanfics cover a wide range of ideas, some of which are quite out - there. However, this idea seems rather extreme for the Batman universe. Batman is usually a protector, and killing Robin's parents would be a huge departure from his normal values. If it exists, it's likely a very niche and perhaps controversial piece of fan - created work.
Perhaps Aramis is a character in a story or a group of friends where this trait of not being into fanfic has been defined. Maybe in a community of book lovers or media enthusiasts, Aramis stands out as the one who refuses to engage with fan - created content. It could be that Aramis has a very academic or traditional view of literature and media, and fanfic doesn't fit into that view. So, they are known for 'not eating' fanfic.
One interesting idea could be the reaction of Gotham's citizens. They might be shocked to learn that the wealthy Bruce Wayne is Batman. Some might feel betrayed, while others could see it as a sign of hope that someone so privileged is using his resources to fight crime.
Maybe there's a villain who discovers Robin's identity and uses it against him, while Batman is clueless. Batman then has to figure out what's going on and why Robin is being targeted without knowing his true self. This would create a lot of action - packed scenes as Batman races to save Robin.