Any time there's a special feature on a bone, usually a muscle attaches to it. I googled, and found out that the mentalis muscle attaches to the chin.
Interestingly, wikipedia says "In conjunction with orbicularis contraction, the mentalis muscle allows the lips to 'pout.' Externally, mentalis contraction causes wrinkling of the chin skin, as used in expressions of doubt or displeasure. It is sometimes referred to as the 'pouting muscle.'" [Emphasis mine]
Humans have complex facial expressions, and I would say that the pout is part of the repertoire. When someone is pouting, they are in extreme emotional distress, on the verge of sobbing. Having such an obvious "tell" would be beneficial to a social species, probably leading to conciliatory behavior and promoting de-escalation and group cohesion during conflict.
I did some cursory googling to see of the mentalis is involved in speech production, but found nothing at my level. Offhand I can't think of any particular speech sounds I can make when my lips are in pout formation.