Reid aside who truly want to learn the magic inside him and Elira want to help him learning it, Elira have obligation since she's a noble and reid need to have education since he's Elira fiancee i think.
Well, that's a fair explanation, but if I were trying to be truly critical of the story, I can think of two counterarguments. For Elira, I think her obligation would be more towards her country, and the country will benefit far more from having her out in the world doing stuff than being in magic school. She's already a person of mass destruction, after all. As for Reid, the person right next to him is probably the best possible person in the world to actually figure out how to teach him magic, and if he was going to marry into nobility, having personal tutors privately instruct him would be much better both in terms of having him learn faster and also not potentially embarassing Elira's family with a public incident due to his heritage.
In either case, the government of this kingdom, if it was aware of either or both of their abilities, should be doing everything in its power to bind them to its service, not have them go through the motions in magic school and potentially deal with some asshole noble that's going to give them any cause to be hostile towards the rulers or influenced by foreigners who might tempt them into sympathy towards other peoples. To be fair, however, that kind of lack of realpolitik sophistication is common in a lot of similar manga (Black Bullet and Scientific Railgun come immediately to mind)