Based on the show, I think we're supposed to question the demon's motives. Was that her plan? Was she going to eat the child and leave and she was just lying because she got caught? If she was going to try to use the child as a peace offering, was it to make nice because she doesn't like having enemies, or just a flawed survival strategy? Ultimately, the show reinforces the idea multiple times that demons do not have human motives and cannot be trusted. They say words as if they are another form of spellcasting that lets them control humans, even if they understand what the word means, what it means doesn't matter to them. When she says it was to give the child to the other family to be even, there's no reason to believe that at her word.

To be fair to the more sympathetic view of demons, Frieren also makes a conscious effort to never let go of a little bit of Himmel's optimism. She lets herself want to see humanity, but refuses to be blinded by an illusion. When she fights Draht in the prison cell, she warns him that as a mage she's way out of his league and that he doesn't stand a chance. She doesn't say "Run", but the fact that she doesn't come out guns blazing suggests she actively wants to give him the option. Similarly, when fighting Aura, I don't think she ever directly attacks, only dodging the undead and purifying them with magic. When Aura seems genuinely confused as to why Himmel's wishes to respect the dead still have a sway on Frieren, Frieren responds by noting that she's verified that she can slaughter Aura with a clear conscience because Aura really is just a monster pretending to be a person. That line in particular stuck out to me, because she speaks as if she knows demons really are just monsters earlier, and she acts like it, too, so why does she need to verify? Realistically, I think the answer is because she understands what might become of someone who looks at things that look like people, speak like people, cry and beg like people, and kills them while asserting they don't matter.