"Every witch and wizard has a special set of genes; some that allow for the ability to breed outside of their own species, creating mixed species, others can provide healthy offspring to the same person who helped provide them with their own life, and plenty of others. This whole thing of trying to keep blood pure is, while worth it in cases, being that we are in a Purifications Dynasty, it also helps to span things a bit to assure certain lines done get snuffed out.