Social learning mechanisms are usually assumed to explain both the spread and the persistence of cultural behaviour. In a recent article, we showed that the fidelity of social learning commonly found in transmission chain experiments is not high enough to explain cultural stability. Here we want to both enrich and qualify this conclusion by looking at the case of song transmission in song birds, which can be faithful to the point of being true replication. We argue that this high fidelity results from natural selection pressure on cognitive mechanisms. This observation strengthens our main argument. Social learning mechanisms are unlikely to be faithful enough to explain cultural stability because they are generally selected not for high fidelity but for generalisation and adjustment to the individual’s needs, capacities and situation.