To impart knowledge and resolve doubts for others... this in itself is an act that allows both parties to grow together.
Therefore, for Aoto, the greatest benefit of accepting Elodie as his disciple is that in the process of passing on the Natural Reasoning Heart Stream to her, he can also progress along with her, indirectly enhancing his own swordsmanship skills.
But compared to the "gaining," the "losing" of accepting Elodie as a disciple is also quite evident.
The greatest "loss" is, of course, the cost of time.
Aoto is not unemployed, nor a swordsmanship master who exclusively teaches others for a living; he has a formal job at the North Guard Station.
The leisure time he can freely allocate is not exactly plenty, but not scarce either.
Although being Elodie's teacher has certain benefits for his own swordsmanship practice... spending that large chunk of time directly training hard at Shiwei Hall seems to better promote his swordsmanship progress.
