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.
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.
This situation would likely create a lot of tension. Batman is used to knowing everything about his allies. Without knowing Robin's identity, he might be constantly on edge, wondering if Robin has some hidden agenda. For Robin, he would have to be extra careful not to let his real identity slip, which could put a strain on how they interact during missions and in their downtime.