I’m not saying they are not killing birds, or mice, or small preys in general. Cats are predators and amongst the best. What I’m saying is that they are invasive only in places they never were in before human brought them (like Australia or small islands). In continental Eurasia (except areas where they are explicitly been controlled), they have always been there, and the environment is adapted to their presence and will not significantly suffer, not more than any other predator.