We introduce a mathematical model of cultural evolution to study cultural traits that shape how individuals exchange information. Current theory focuses on traits that influence the reception of information (receiver traits), such as evaluating whether information represents the majority or stems from a trusted source. Our model shifts the focus from the receiver to the sender of cultural information and emphasizes the role of sender traits, such as communicability or persuasiveness. Here, we show that sender traits are probably a stronger driving force in cultural evolution than receiver traits. While receiver traits evolve to curb cultural transmission, sender traits can amplify it and fuel the self-organization of systems of mutually supporting cultural traits, including traits that cannot be maintained on their own. Such systems can reach arbitrary complexity, potentially explaining uniquely human practical and mental skills, goals, knowledge and creativity, independent of innate factors. Our model incorporates social and individual learning throughout the lifespan, thus connecting cultural evolutionary theory with developmental psychology. This approach provides fresh insights into the trait-individual duality, that is, how cultural transmission of single traits is influenced by individuals, who are each represented as an acquired system of cultural traits.