Cultural evolution relies on the social transmission of cultural traits along a population’s social network. Research indicates that network structure affects information spread and thus the capacity for cumulative culture. However, how network structure itself is driven by population-culture co-evolution remains largely unclear. We use a simple model to investigate how populations negotiate the trade-off between acquiring new skills and getting better at existing skills and how this trade-off shapes social networks. We find unexpected eco-evolutionary feedbacks from culture onto social networks and vice versa. We show that selecting for skill generalists results in sparse networks with diverse skill sets, whereas selecting for skill specialists results in dense networks and a population that specializes on the same few skills on which everyone is an expert. Our model advances our understanding of the complex feedbacks in cultural evolution and demonstrates how individual-level behavior can lead to the emergence of population-level structure.