It is frequently claimed that breeding animals that we know will have unavoidable health problems is at least prima facie wrong, because it harms the animals concerned. However, if we take ‘harm’ to mean ‘makes worse off’, this claim appears false. Breeding an animal that will have unavoidable health problems does not make any particular individual animal worse off, since an animal bred without such problems would be a different individual animal. Yet, the intuition that there is something ethically wrong about breeding animals — such as purebred pedigree dogs — in ways that seem negatively to affect welfare remains powerful. In this paper, an animal version of what is sometimes called the non-identity problem is explored, along with a number of possible ways of understanding what might be wrong with such breeding practices, if it is not that they harm the animal itself. These possibilities include harms to others, placeholder arguments, non-comparative ideas of harm, an ‘impersonal’ approach, and concerns about human attitudes and dispositions.