The European Union (EU) set clear climate change mitigation targets to reach climate neutrality, accounting for forests and their woody biomass resources. We investigated the consequences of increased harvest demands resulting from EU climate targets. We analysed the impacts on national policy objectives for forest ecosystem services and biodiversity through empirical forest simulation and multi-objective optimization methods. We show that key European timber-producing countries – Finland, Sweden, Germany (Bavaria) – cannot fulfil the increased harvest demands linked to the ambitious 1.5°C target. Potentials for harvest increase only exists in the studied region Norway. However, focusing on EU climate targets conflicts with several national policies and causes adverse effects on multiple ecosystem services and biodiversity. We argue that the role of forests and their timber resources in achieving climate targets and societal decarbonization should not be overstated. Our study provides insight for other European countries challenged by conflicting policies and supports policymakers.