OK, so I've heard stories like this one before, and I think I might be onto something with a particular hypothesis.

You know cuckoos, right? They're brood parasites, which means that the female doesn't care for her own eggs. She finds another bird's nest, dumps her egg into it, and when the egg hatches, it gets raised by the owner of the nest. A lot of birds don't even recognize a baby cuckoo as something different, so they'll just keep feeding it.

What I think is going on in these stories is that there's a species, perhaps very closely related to us, that's a brood parasite of humans. They use us to raise their offspring, the same way cuckoos use other birds.

I've been reading up on these creatures too, and based on the above information, I can't help but feel that they aren't predators. They're brood parasites.

You know how cuckoos lay their eggs in other birds' nests, and when the eggs hatch the mother bird takes care of the baby cuckoos as if they were her own? That's actually not an uncommon tactic in the animal kingdom. Several species of wasps lay their eggs in the nests of bees and other wasps, and there are even catfish that place their eggs in the mouths of tilapia fish. Maybe Fleshgaits are like that, but with humans.

In medieval Europe, people believed in something called a Changeling, where if a child started behaving strangely, it was said to have been taken away by fairies and replaced with a copy. I think that might have been based what Fleshgaits do, and what OP here is referencing. These creatures are closely related to humans, and evolved to use us to raise their young, hence their physical similarity to us and their uncanny ability to mimic our speech.

Scientists call this kind of behavior brood parasitism. In other words, I think a lot of the Fleshgait's traits-- its humanoid appearance, its ability to mimic speech, its low numbers, and its fixation on children-- could be explained if it's a brood parasite of humans.

Headcanon time: This is what they look like to the kids they scare. The "friendly" versions we see in the movie are just how they see each other.