Cultural evolution relies on the social transmission of cultural traits across a population, along the ties of an underlying social network that emerges from non-random interactions among individuals. Research indicates that the structure of those interaction networks a ects information spread, and thus a population's ability for cumulative culture. However, how network structure itself is driven by population-culture co-evolution remains largely unclear. We use a simple but realistic model of complex dynamic social networks to investigate how populations negotiate the trade-o between acquiring new skills and getting better at existing skills, and how this trade-o , in turn, shapes the social structure of the population. Our results reveal unexpected eco-evolutionary feedback from culture onto social network structure and vice versa. We show that selecting for generalists (favouring a broad repertoire of skills) results in sparsely connected networks with highly diverse skill sets, whereas selecting for specialists (favouring skill proficiency) results in densely connected networks and a population that specializes on the same few skills on which everyone is an expert. Surprisingly, cultural selection for specialisation can act as an "ecological trap" where it can take a long time for a specialist population to adapt to a generalist world. Our model advances our understanding of the complex feedbacks in cultural evolution and demonstrates how individual-level behaviour can lead to the emergence of population-level structure.