>The children "argument" is from the site - it is a rhetoric figure (or fallacy) probably hoping to evoke non-thinking, only emotional response, turning me off.

I didn't read the url , but the "children" might not be a fallacy if there is substantial combat taking place.
For example - I read recently that there are hundreds of thousands of widows in Afghanistan and Pakistan whose husbands were lost in all of the endless fighting there.
Killing off fighting-age men disproportionately increases the number of women and children in the population.