The problem with this question is that it is badly formulated. Therefore, it doesn’t really make sense which means it is difficult to answer. If it was well formulated it would still be difficult to answer (for me at least) 😉. I’ll have a stab at it. But it will be an overview.
Above: the litigon is a second-generation hybrid from a female tigon and a male lion, specifically an Asiatic lion.
The reason why different species cannot mate with each other is because of various barriers. One of them is simply mechanical i.e. the difference in size. Others will be the fact that from a purely physical point of view it’s impossible for them to mate. Or, in the wild they never meet. However, the biggest barrier which makes it impossible on occasions is because their chromosomes don’t ‘match’ or are incompatible. Different species have different numbers of chromosomes and so genetically it is impossible for them to mate.
Sometimes they can mate but that the male offspring is sterile. It’s a kind of halfway house where you get an offspring but they can’t procreate. This happens with mating a serval with a domestic cat to produce the F1 Savannah cat. These are different species of cat producing a wild cat hybrid.
RELATED: Are ligers real and natural?
So, whether two different animals can mate and breed depends upon their taxonomic classification and whether they are in the same species or the same genus. A genus is one step up from species in taxonomic classifications. If they are the same species, they can mate but if they are of a different genus they can’t in general. In other words, it depends how far apart they are in terms of their genetic and physical make up.
Now back to the question. All cat breeds are the same species so they can mate and produce hybrids. But the domestic cat is of the genius Felis while the tiger, for example, as of the genus Panthera. No one has tried to mate these species of cat. It is a mad thought although I am sure someone has considered it. It is physically impossible but technically possible by artificial insemination. But it has not been tried to the best of my knowledge (wrong? please leave a comment) and it would not produce offspring.
There is an article on The Dodo website about a domestic cat carrying the embryo of a tiger in order to improve tiger conservation. But this would not be a straight case of artificial insemination. The scientists, Dr. Franklin West, who proposed it was going to create stem cells from the skin cells of big cats and then use those cells to make a sperm and an egg. It’s highly technical and it tries to circumvent the impossibility of natural mating.
The F1 Bengal cat is a cross between the Asiatic leopard cat which is of the genus Prionailurus and a domestic cat which is mentioned as of the genus Felis. These two cat species of a different genus can mate but the offspring is sterile.
You can cross lions with tigers and lions with leopards, for example. They are different species and you produce hybrids (see link below as one example). These cats are of the same genus, however.
RELATED: Are tigons fertile?
All domestic dogs are of the same species. They are different breeds but all breeds fall within the umbrella of one species, lupus. The same rules apply to cattle. Yuki (see below) is at the Shy Wolf Sanctuary in Florida. He is a massive triple wolf hybrid. His DNA is a mix of three different canine types: 3.9% German Shepherd, 8.6% Siberian Husky, and 87.5% Gray Wolf.
To emphasise, cats, dogs, horses and cattle can be of the same species and these can crossbreed. The same applies to birds, fish and reptiles but it doesn’t happen in the wild i.e. naturally. When it does happen, it is normally because of human intervention. This is when people out of curiosity crossbreed different species of animal.
However, they are stepping outside of the bounds of naturalness and in doing so you end up with undesirable or unexpected results such as sterility if it works at all.