I think that you can tame a lion or a tiger if you get it as a cub. But it is still a lion or a tiger and it will most likely act like one at some point. If you breed it with another of its kind and raise them away from its dam, they will still be lions or tigers, though they may not have the same fear-respect of humans.
Some critters take to domestication easier than others. In the cat family, there are domestic cats, and there are wild cats. In the dog-family there are wild dogs and there are domestic dogs.
I think that cats and dogs are fundamentally different in some ways though, or at least some cats and some dogs. Many wild cats are more singular. Only domestic cats and lions seem to pack up. I think for this reason, cats in general rely more on instinct than on training within a pack environment. Though the dam does train her cubs, so I am not sure how that fits. But if you welp some wild cats, and keep them for six or eight months and then release them into the wild, the chances are, they will probably revert to the wild easier than, wild dog or wolf pups whelped and raised by people.
I guess my opinion (which if added to a dollar will probably buy you a cup of coffee), is that it is some of both. I think there are wolf/canine breeds that lend themselves more to domestication than other breeds, and these breeds did hang around the garbage dumps, much like bears will, gathering off of human's leavings. As we do when we come across a wild raccoon cub or other baby animal, humans probably raised them when they would find them helpless. Dogs being very dependent on the pack quickly packed with humans, and when these semi-domesticated wild dogs bred with others, the pups were raised, and they quickly learned a new type of life.
Other wild dog and wolf breeds were not as likely to be close enough to the humans to give themselves over to domestication, or they were not wired for it.
I do not believe these animals were immediately given member-of-the-family-status. I think that they attached themselves to a human and hung around their dwelling, following them on the hunt, roaming with them, and living mainly on whatever was thrown away. Through the ages, people started to find those things that dogs were good at and started selectively breeding for those traits.
Jenna, RN CGC & Babs, CD RA CGC HIC
Heidi, RA CGC
SG3 Odessa, SchH1, Kkl1, AD
Ninja, RN CGC & Milla, RN CGC
Joy, Star Puppy, RN CGC
Dolly CGC & Bear CGC