I find beauty, at least intellectual beauty, in all species. I regret the loss of any species, save the likes of the polio virus, and especially of those species I am more familiar with. The loss of a species is like the loss of a piece of art. In both cases we are losing a bit of history, an instance of superior design, or a source of amazement.
The death of an individual organisms is very different from the extinction of a species. We regret the death of animals or plants that we have become acquainted with in a similar way that we regret the death of human acquaintances.
We human beings assign an intrinsic value to the life of other human beings. We say that all humans have the right to life. In a very limited way we extend this right to other organisms; most of us prefer to live in a world where humans have at least some respect for the lives of other individual organisms.
Whether groups of humans have an intrinsic value and a right to exist independent of the value and rights of individuals is quite another matter. I do not support such value and such right. I do not think, for example, that the white race, if such thing exists, has intrinsic value and a right to exist. Humans that happen to have blue eyes have intrinsic value and we must respect their lives. The set of humans with blue eyes has no intrinsic value and no rights. By the same token I assign no rights to "peoples," nations, cultures, languages or religions, but I believe in the rights of individual human beings to identify with whatever culture, to speak the language of their choice or to practice their religion.
Following the same logic, I might accept some sort of rights for nonhuman individual organisms, but not for species, which are sets of organisms. I do not think that populations, varieties, subspecies, species, families or orders have any intrinsic value and a right to exist. I want them to exist because I and many other people enjoy the diversity of life.