Animal behaviour is often shaped by learning. Learning can occur individually by trial and error or exploration, but it can also occur by observing others (social learning). When information passes from one generation to the next via social transmission, animal populations may develop culture. Culture often manifests itself as idiosyncratic local population behaviour. Classic examples include nut cracking in chimpanzees or whale migration patterns. Culture provides fitness benefits, such as access to important resources and influences key population dynamic parameters. Over the past decade, there has been increasing realisation that social learning and culture in animals play important roles in their conservation. We have known that fishes are capable of social learning and develop culture, particularly in the context of migration routes, for more than two decades yet fisheries management practices have tended to ignore this fact. Here we propose that our present fisheries management models, which tend to focus on maximising sustainable yield largely by setting minimum size limits and quotas, not only ignore the importance of social learning and culture in fish biology but actively target the very individuals that likely store cultural information; large, old fishes (LOFs). In effect, present management strategies encourage cultural genocide. The destruction of animal cultures can lead to rapid collapses in local populations and recovery periods tend to far longer than standard population models predict. Once gone, culture is very difficult to replace which explains why populations of long-lived fishes take so long to recover even after lengthy fishing moratoriums.