Despite emigrations’ adverse impacts on several EU Member States, especially in Central Eastern Europe, topics like brain drain and depopulation have received relatively little attention at EU level compared to concerns associated with free movement and immigration. This article offers an answer to why this is so. Drawing on agenda-setting theory, it argues that the institutional framework of the EU both inhibits and disincentivises attempts to turn emigration into an EU level topic. Seen through the lens of the EU policy, regulating emigration becomes a matter of cohesion policy, which makes it both difficult and unattractive to lobby. To assess the argument empirically, the article draws on elite interviews with national and EU policymakers and document analysis from 2010 to 2023. The analysis reveals a structural bias of the EU and offers an example of how pertinent political issues fail to become EU topics.