Okay, the flying cat thing is pretty funny, mostly because it's not real. But make no mistake, the vast majority of these hybrids are not "bred" - no, a Begal Tiger and a short-haired tabby did not breed. Eggs or sperm were harvested from each, in-vitro fertilization was done and the embryos developed in a petri dish, the few chimeras that developed from many attempts were implanted into a surrogate mother, very few of those actually implanted into the uterus, and the vast majority of any fetuses that began to develop died before or shortly after they were born. It is likely a fair number of Mothers also died in the process.
Honestly, it's interesting from a scientific perspective but I don't find it all that entertaining.