There might be a fellow student who has a crush on Izuku, believing her to be a boy. When the truth is revealed, this character could turn into an antagonist out of anger or betrayal, causing problems for Izuku both personally and in her hero training.
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.
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.
Perhaps a rival adventurer who discovers Bilbo's secret and tries to use it against her. This antagonist could be jealous of Bilbo's place in the group and sees her secret as a way to undermine her and take her position. He might spread rumors or try to create situations where Bilbo's secret is likely to be revealed.
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.
There's also a possibility that the main antagonist is another student at U.A. High School. This student could be competitive and feel threatened by the girl's relationship with Izuku. They might use underhanded tactics to try and make the girl fail or lose her confidence, adding a layer of drama and conflict to the fanfic.
Perhaps a jealous rival. This person might be a male who is threatened by Ed's success or popularity. When they discover Ed is a girl, they could use this secret to try and drive her out of the group or community she's in. They might spread rumors or create problems for her.
Maybe there's a dark wizard who has a vendetta against Natsu's family. When he finds out that Natsu is secretly a girl, he sees it as an opportunity to further his evil plans. He could try to kidnap her or use her as a bargaining chip against her family or friends. He might think that because she's a girl, she'll be easier to manipulate or capture compared to if she was thought to be male.
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.
The Cullens could potentially be the main antagonists. Since Bella is secretly a Volturi fan, the Cullens' views and actions that oppose the Volturi might be seen as obstacles in Bella's new - found admiration. For example, if the Cullens try to keep Bella away from Volturi - related things, they would be acting against her interests.
Maybe there's a villain group that targets Izuku specifically because of his money. They want to steal his wealth to fund their evil schemes. They might try to kidnap him or hack into his financial accounts. Izuku then has to use his wits as well as his money to outsmart them.
Maybe a mechanical tyrant in a steampunk - inspired setting. This tyrant has created an army of mechanical beasts and is trying to rule the city. Pyro, as a girl with fire powers, is the only one who can melt the metal parts of the beasts and stop the tyrant. The tyrant sees her as a threat to his rule and is constantly trying to eliminate her.