Not One, But Seven
Determination was an entity that almost all humans possessed from the day they were born. Monsters, however, had to gain it through certain actions or they simply would not have it. This could be viewed as a positive thing; most monsters were afraid of this powerful force they couldn't understand. It took someone who possessed a virtually empty soul to gain determination, someone who'd either lost everything or never cared what they'd had.
Monsters never would have suspected him. He was so kind, so gentle with everyone. People called him a pushover and spoke fondly of him regardless of his lack of being able to name. But Asgore knew he'd gained some determination, some LV, some EP, something that wasn't as kind or cuddly. He lost two children due to his original disposition, so he killed his old self.
Chara was the first human child, not the last. He'd let not just one human child die, but seven.