The importance of syntax is that it creates a treelike set of rules of reference that enables us to communicate quickly - who did what to whom, where, when, why and how. Children acquire syntax effortlessly by listening. Social life perhaps is the key to providing individuals with the chance to mimic and learn useful ways to adapt. Useful discoveries by one individuals can be passed on to others via socializing. Anthropologists recognize primates to be highly sociable creating a vehicle by which to pass on meaningful behaviors that enhance our ability to survive.
Language is something that requires both physical and mental capacities to merge.
One must remember that there is a process of selection that would operate on our ability to create this breakthrough. First, the genetics must be present. Second, copies of these must be made and passed on to subsequent generations. Thirdly, one would assume that further variations would be created through mututions that continue to accumulate. Fourth, these variants would compete with relative success measured in terms of how frequently they are passed on to the next generation.