Personally, I think that Fire Nation itself focuses very much in power and strength. In my head!canon, injured soldiers (I mean somehow permanently and seriously) are put behind the lines and somewhere...harmless, because they are 'weak'. Sick children are considered bad luck, etc. And in this universe, where Zuko lost his leg and he cannot (atleast yet) fight well enough, she considers him weak and useless, and throws him away.

Also, in my head!canon seriously crippled (btw, is that a 'good' word? Or is it insulting?) soldiers usually kill themselves very quickly afterwards.

Hopefully I made some sense...