
Imo it's because he's still not strong enough. If he teaches his sister magic,
1. It's very unlikely she'll become strong so soon.
2. The fact that he knows magic (and she's learning it) may be exposed, drawing attention and enmity. MC isn't strong enough to deal with everyone yet.
3. She may also reveal it herself accidentally by using magic in front of people. Imagine if she slipped off some height or something and accidentally used wind magic or something.
Also, if he only teaches his sister right now then the for the enemies, the targets will be singular. A magic academy on the other hand means that by that time MC will be sufficiently strong enough (otherwise he wouldnt have dared to open the academy).
Of course it could also be that the sis has no mana or that MC didn't teach her yet because he was hiding the fact he could use magic and he hadn't taught her after the reveal because he didn't get the time yet.
He eventually wants to start a magic academy to spread magic. So I was wondering why doesn’t he teach his sister magic? That would also be a great way for her to protect herself if need be.
Also the emperor and the sister are just too cute!! Like I can’t wait to hopefully see them together one day!