The main reason not to have hybrids: to maintain the genetic composition of a successful species that has evolved naturally.
This isn't a case of pureblood/line-bred breeds of organisms. Dogs of every breed and every combination of breeds are the same species, there's no hybridization going on there. It's not entirely about preference, but many people do have a preference for pure species. It's more about maintaining the species and conserving the natural genetic uniqueness that makes them a species.
Hybrids do not kill the parent species. Hybridization simply creates the opportunity for accidental or deliberate destruction of the the pure species as animals change hands and are bred. Individuals within colonies do not live forever--as they die, their offspring are continue on. If you introduce hybrids into a colony, you'll eventually have only hybrids. Since hybrids have genes from both parental species, you have new gene combinations--these gene combinations may not appear right away and could take several generations to appear. Say one such gene combination causes a high chance of failing to develop into adults--this could mean that not only have the parental species been wiped out of the hobby, but now the hybrids that overtook them will also eventually die out as colonies collapse.
It's not unheard of or uncommon to create hybrids--many scientists hybridize in order to discover how genes from closely related species interact when hybridization occurs. What isn't okay is for those hybrids to be dispersed throughout the hobby where people may unwittingly breed them and introduce them into colonies of the pure species and potentially cause what I explained. Hybridize if you wish, but please do not trade, sell, or give them away. All it takes is for someone to forget what they are and distribute them.
I suggest taking a course on genetics to gain a better understanding of species, hybrids, and how the introduction of new genes into an existing gene pool can effect a population.
