"kill children if they're from the Bad Group."
The point is, though, it's not a child. It's not a "bad group." It doesn't have emotions. It is a predator which exploits your empathy in order to kill you. You don't think twice when the group kills bloodthirsty wolf monsters or slimes or giant carnivorous plants, but when the monster can talk and pretend to have emotions now it's a problem. That's exactly what it's betting on.

Because that's what they do, they mimic emotions. They don't turn it off when in private because they aren't scheming people, they are monsters that mindlessly mimic human behaviors. They act like people when they're in private and when surrounded by others of their kind because all they know how to do is act like people. The same way a mimic acts like a treasure chest when there are no people around. It's not a person who decided to act like a treasure chest, it evolved to act like a treasure chest because that's what allowed it to eat people.
But you can't believe that it would be possible for a creature to exist which similarly lacks those mental faculties but appears to have them?
This is all addressed in the story. There are monsters everywhere on the spectrum from something like a slime that doesn't appear to have any complex thought to a demon that could convince you it has just as complex an inner world as a human. There are monsters out there which aren't convincingly human but have mastered speech to lure people into their clutches. There are more primitive forms of those who can make noises that kind of sound like speech, or form only a few words. Demons are just the most evolved form of an ecological niche whereby human empathy is exploited to hunt them. They are literally no more internally complex than slimes, they're just good at convincing you otherwise.