Horses and zebras are the same thing, just different variations (rather liked a mixed-race human couple). Ligers exist because all cats are compatible with one another (size permitting), just as all humans are compatible regardless of race or colour
Cats and dogs are as different from one another as humans and apes, so the potential for inter-breeding just isn’t there.
There are human chimeras, but they are humans with more than 2 sets of human DNA.
https://www.insider.com/what-is-a-human-chimera-and-how-does-it-happen-2017-11
I think the question you’re asking is why are there not human/non-human hybrids.
In which case, there is. Homo sapiens also bred with other proto-humans, and their offspring still live today.
https://en.m.wikipedia.org/wiki/Interbreeding_between_archaic_and_modern_humans
(Sorry i’m in a rush so i couldnt get you a better source – but some links are there)
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