Yes, mozz, mules are often sterile, but not always. Female ligers are usually fertile, while males aren't- probably as much as I know! But the point is, they can breed and breed, add in a panther, they can also breed with. And you can end up with an entirely new species.
The categories we use, are purely about whether animals can breed together or not- so saying they are part of the same family, is irrelevant, because that is how we chose to classify them in the first place.
I'm quite shocked tbh, that theland didn't seem to realise mules can breed- while clearly overriding scientists who do know.