An important aspect of human uniqueness is an unprecedented behavioral and mental flexibility allowing us to for instance learn to play musical instruments and master mental arithmetic.
Flexibility in general offers opportunities for adaptation and development but it also comes with substantial learning costs that quickly tend to overshadow such benefits. These learning costs are mainly caused by a combinatorial explosion of possibilities. In animals this problem is solved by genetic guidance of decision making and learning but this also substantially reduces flexibility. However such genetic guidance odds with human flexibility, and cannot explain many human unique phenomena because they emerge on a time scale that rule out genetic changes as the explanation.
I will instead suggest that in human culture and cultural evolution, culture play a similar role as genetic guidance in animals and that is what allows us to be super flexible. This hypothesis also suggests that human uniqueness to a large extent is a product of culture evolution rather than genetic evolution. This includes for instance many aspects of thinking, social learning, language and cooperation. It also suggest that the relevant genetic changes that made us different are few but decisive and may have occurred a rather long time ago.