Commonly, the justification for using magical child soldiers is that they're more powerful than your adults. E.g. in Nanoha you can have freakish superpowered prodigies more powerful than most people alive. In Railgun, you don't have soldiers per se, but the setting conceit of advancing 'esper' training means that at the moment, your most powerful people (outside of the 'magic' world) are teens; current adults were too old to get the neat training. In Symphogear, it's not clear why all the Gear users are teen girls (though some of them were experimental orphans), but they are, so you use them. I assume Simoun had a reason for using pre-Change 'girls' as pilots, though don't really remember.
We got a hint of that being true here (more explicit in the anime version than in the fan TL of the manga, with a line about students being more effective than soldiers), but given the long age of magic in the setting, and lack of other worldbuilding, it's hard to see why 16 year olds would be peak fighters.
Of course the other reason is that you're just that desperate for soldiers.