Thinking about her training focusing on an absence rather than her main strength brings something immediately to mind: he wanted her to be a hero, like the actual class.
Heroes have great physical strength, offensive magical capabilities, and can even use healing magic. Maam already had 2/3 from her parents, so Avan wanted her to be able to Dragon-Quest-1-it if need be.
Not to mention, even if he didn't specifically have hero skills, Hyunkel was clearly reaching a level where he could adventure independently, and Avan knew that. Substitute a magic gun for plenty of herbs and you've got another psuedo-hero. It wasn't until he had a student that was actually hero-class that he got close to his ideal, and even then he still couldn't use healing magic.
