Actually, lets take this a step back. What language did you read Asunder in? I'm curious if there's some sort of breakdown in communication or something. It's never implied that Cole kills children in the English version.
The English version. Where it says :
"I didn't mean to burn it down," she whispered through ragged breaths. "The fire came out of my hands, but I don't even know why. It all happened so fast, I tried to warn them...."
That's the little girl describing what would have been her first experience using magic. Even though we know it's a lie, it's a lie that only works if she was of the age that magic first manifests: puberty.
"Are you a mage, then?" she asked. "They said a mage would come."
That's the child indicating she has been informed she is not to be summarily executed, but judged first.
"I'm...fading away," he muttered. "I can feel myself slipping through the cracks. I have to do this, I'm sorry."
That's Cole explaining to the little girl that he's going to kill her no matter what.
The exchange after that I've posted on numerous occasions. It's Cole selling the idea of killing her to its victim. She responds by confessing that she murdered her family, but the context of that confession is also intriguing. She thinks Cole is a demon come to possess her. Maybe she sees becoming an abomination as a means for survival. If she could convince the demon she was enough of a badass, it might possess her, perhaps making her strong enough to maybe break out. It is a separate conjecture.
The facts are, that that was a little girl, even if she's never called a child specifically, and that Cole was going to kill her, whether he convinced her to do so without resistance or not.