A hybrid is a cross between two species. For example, you can cross two kinds of plants, or a coyote and a wolf could interbreed to create a hybrid.
The term "parahuman" to mean a 'Human-animal" hybrid is a bit odd and doesn't really make sense, since humans ARE animals. Specifically, we are mammals--that is animals with fur and mammary glands.
In general, hybrids can occur naturally between closely related species, but not between species that are only distantly related. Our closest relatives are the other
great apes--the chimpanzees, bonobos, orangutans, and gorillas. To my knowledge there are no documented cases of a human hybridizing with another ape.
I don't know if it's physically possible or if anyone has secretly tried it. I have often wondered about this. People involved in fertility research might have some insights into this.