I'm kinda worried that sensei only has one wing
Yeah. No matter what Izumi has been called due to her ears, it's still worse to ask Succubus-sensei if she can fly, when she has lost one wing. Flying is something mankind has dreamed of since the ancient times, and holy things like angels are depicted with wings, not to mention bird images are very popular decorations. So, if one used to be able to fly, but then can't anymore due to an accident, it's quite low to tell her to fly suddenly. It's like asking a paralysed person trapped in a wheelchair why they won't get up and run.
All that being said, Izumi is a bullied kid, to an extent, so it's understandable she wouldn't have the will to care about others when she herself feels hurt.