She was a pureblood royal and the homeroom teacher of Anos' class.
Due to being royalty, Emilia was extremely prejudiced against her mixed-blood students, whom she saw as filthy beggars scavenging for scraps of her lessons. She had no qualms about injuring or even killing them if they caused problems for her. This put her in conflict with Anos, who was extremely talented despite being a mixed-blood. Even though he proved himself, she still felt like Anos had no business questioning or surpassing royalty. She was willing to sabotage him to satisfy her standards, as shown when she attempted to ruin Anos' perfect score for the dungeon exam and when she tried to steal his sword during the Demon Sword Tournament.
(Source: Maou Gakuin Wiki)