Well, it depends on how the author of the fanfic has characterized Figure 13. However, if the premise is that Figure 13 is a girl in this fanfic, then that's how it is within the context of that particular story. Different fanfics can have different interpretations and characterizations, but in this one, it's stated that Figure 13 of Izuku is a girl.
She could be an ordinary girl who just happened to be at the right place at the right time and caught Izuku's eye. Maybe she was at a hero event and Izuku noticed her kindness towards the other attendees.
Well, it could start with Izuku waking up as a girl one morning with no explanation. He (now she) tries to keep it a secret at first but then realizes it's not possible. The story could focus on how Izuku's relationships change. For example, Bakugo might initially tease her more harshly but then come to respect her in a different way. And Midoriya could find that she has a different approach to using her quirk as a girl, maybe being more strategic or having different physical capabilities that she has to learn to master.
People write 'izuku is a girl' fanfic because it offers a fresh perspective on the original story. It allows them to explore different character dynamics and plot possibilities. By changing Izuku's gender, the interactions with other characters, like Bakugo or All Might, can be re - imagined in new and interesting ways.
A great 'izuku is a girl' fanfic could focus on her relationship with other characters. Maybe she has a closer bond with Ochaco as they are both girls now. They could support each other more in their hero training, and Izuku could also inspire Ochaco in different ways. It could be really interesting to see how the dynamic between the characters changes with this gender swap.
In the 'izuku becomes a girl fanfic', perhaps the plot involves Izuku adjusting to her new physical form. She might struggle with things like different clothing styles and how society views girls in the hero world. Also, her relationship with other characters could change. Her friendship with Ochaco might become more complex as they now have more in common as girls. And Bakugo might react in a really interesting way, either being more protective or even more competitive towards her.
In the 'izuku secretly dating a girl fanfic', the plot could be that the girl is actually from a rival school. Izuku is initially hesitant about the relationship because of the potential conflict of interest. But their feelings for each other are too strong. They date secretly, and there could be some close calls where they almost get caught by classmates or teachers from either school.
It could be a character who somehow discovers Izuku's secret and tries to use it against her. Maybe a rival at school who is jealous of Izuku's progress and sees this as a way to get her expelled or discredited in the hero community.
Maybe the story could focus on how Izuku, as a girl secretly, has different perspectives and experiences compared to her male counterparts. She might face unique challenges in a male - dominated hero society, like having to prove herself even more. And there could be a sub - plot about her developing a romantic interest in another character, but being hesitant because of her secret.
Perhaps a jealous classmate who has always been in Izuku's shadow. Now that Izuku is a girl, this classmate sees an opportunity to undermine her. They spread rumors about how Izuku's transformation is some sort of cheat or that she's not the same reliable person she was as a boy. This classmate's actions and attempts to sabotage Izuku would make them the main antagonist.