This innovative mixed methods network study with young refugees in the Netherlands disproves integration policy assumptions that language acquisition is key to social integration and that social integration is about gradually increasing contact with native citizens, or when integration is lacking, about limiting contact to one’s own ethnic group. The study connects the research approaches of government-commissioned quantitative integration studies, which generally reflect the above assumptions, and qualitative studies with migrants, which reveal an ‘integration paradox’ and a ‘doubleness’ of language acquisition generating both inclusion and exclusion. First, it includes the use of languages and countries of origin in ego network data to examine the relationship between language acquisition and social integration. These network data show that participants speak Dutch with most of the diverse non-Dutch people in their networks and have relatively few connections with Dutch natives. Second, to help us understand these findings, participants were asked to share their ‘network stories’. These stories place the network findings within the context of contradictory asylum and integration policies and negative discourse, thereby revealing that with regard to learning Dutch, participants are caught not in a paradox but in an aporia: damned if they do, damned if they don’t.