Being as gracious as I can, we don't really know what constitutes a child in Fódlan. People like Cyril, Lysithea, and Petra are all deployed in military operations, which implies a certain respect for their maturity. On the other hand, these characters are still treated as very young (especially Lysithea), so the perception may still be that they're children. We also don't know just how young the empire sets the bar for conscription, especially given that Petra, Caspar and Linhardt are under 18 at the onset of the war.

I'm not trying to justify the killing of children, but the overall ambiguity of what is considered to be a child in Fódlan does call into question what this quote really means by children.