As far as I know, humans are the only animals with chins. Despite attempts to link them to muscle attachments and other mechanical uses, nothing really convincing has emerged.
I myself think that Desmond Morris had it right, and many of our traits really are sexually derived and are a sort of sexual signaling. A lot of people don’t buy this, but I haven’t heard any convincing arguments against it. Mandrills have bright red noses and blue “cheeks”, and have red marks on the penis and blue scrotums. It seems likely that the facial coloring is a duplicate of the genitals
The Proboscis Monkey is the only one that has a large nose, even exceeding those of people. It also has a bright red penis: http://www.alaskabearsandwolves.com/the-wildly-bizarre-proboscis-monkeys-of-borneo/ The nose is significantly larger in the male.
Although other reasons have been given for these features of these monkeys – which are secondary sexual characteristics, are different for the male and female, and clearly play a role in sexual selection, it seems to me highly likely that the appearance alone of the brightly colored male mandrill nose and face and the large nose of the male proboscis monkey are obvious sexual signals and mimics of the genitals.
So why not with people? The nose is a penis mimic and the chi a testicle mimic. Women with small noses and chins are often considered more attractive (“button” nose), while males with cleft chins – like the double scrotal sac – are considered handsome, and a prominent nose in a man is not a detriment.
There’s a limit, of course – really big chins aren’t considered sexy, nor are really long noses. But the fact that people care at all about that cleft chin and prominent nose should tell us something.
I doubt I can speculate better than an expert, but I would wonder if it gives us room to store our fat tongues, which we use for speech as much as for eating.
After the chin, came the overbite. 900 years or so ago for the Chinese, but only 2½ centuries for the rest of us. It is generally assumed that this is because we started using utensils to eat with and stopped tearing the meat off the bone with our teeth. This is not a genetic thing though, it is just an adaptation.
Reading the Wikipedia article makes some basic points.
What I read decades ago was that it was in response to going to a cooked meat diet. But that doesn’t explain why Neanderthals with a similar diet didn’t have such chins.
Take you pick: speech related, sexual selection (for both sexes) or something else.
The Inuit would seem to be a counter-example of that - their men tend to have little in the way of beards.
Or it could be that beards are one way to adapt to cold chins, just not a universal one. Evolution isn’t perfect, far from it - it’s a collection of jury-rigging and “just good enough”.
Or it could be that beards are a sexual display feature in humans.
I don’t know. That would mean that the one genetic chin mutation trumped out over the entire population of non-chin having sapiens - with no evolutionary (“fittest”) advantage. Possible of course, but highly unlikely, imho.
You need to look into something called the founder effect. That sort of thing happens all the time with small populations or populations that have gone through a bottleneck.
That is a common, layperson’s over-simplification of evolution, which really is ‘survival of the mutations that didn’t kill us or get us killed.’ There is no particular disadvantage to a prominent chin and maybe a cavewoman found it cute so it survived.
One theory is that as our teeth shrank in size the surrounding bone shrank as well, but the lower part of the mandible was less affected, leading to the current prominence. So not that our chins grew, but the rest of our faces flattened out to leave the chins protruding. Perhaps this became a feature of sexual selection, overcoming any later trend to reduce chins again.