While I think causing species extinction is a moral wrong, it is difficult for me to come up with a positive justification for this intuition. The most direct approach is perhaps through biodiversity. But I haven't come across a compelling argument for biodiversity as a moral good either. In fact my intuition appears very fragile on reflection (for instance not all species seem to be on a par, and the extinction of some may seem more devastating than the distinction of others). Any literature reference would be deeply appreciated.
In terms of the morality, it's going to depend how you ground that. Suffering, systemic risk & systemic resiliance, irreversibility, are all specific things to consider. Is all, or some life 'sacred'? Or do we only judge by consequences?
Peter Singer argues that morality is the result of an expanding circle of concern, that we choose not to be gene-machines by expanding our concern from progeny, to family group, to tribe, nation, humanity, to non-humans, to ecologies. Each expansion dignifies us, makes us more fully developed and moral beings.
A case people talk about of extinction being maybe ok, or even good, is malaria/dengue/zika vector mosquitos. It's a good case to consider on 'pro extinction'. Male mosquitoes don't ever bite humans, they pollinate flowers. Mosquitoes are a key prey species for aerial & aquatic ecologies, and by supporting predators, other pest outbreaks are less likely to go to extremes - see the consequences of China's https://en.wikipedia.org/wiki/Four_Pests_Campaign Wider issues of mosquito extermination discussed here: https://www.bbc.com/news/magazine-35408835 How malaria also harms mosquitoes: http://www.sciencemag.org/news/2010/09/how-mosquitoes-fight-malaria Which seems to point toward win-win solutions..
Morals are more-or-less rules-of-thumb, which we allocate consequences to breaking based on a wide range of factors, though mainly risks & harms. It used to be that egg-collectors & other trophy hunters drove the most endangered large predators further towards extinction, and many countries got together to create https://en.m.wikipedia.org/wiki/CITES#Background_and_operation to deal with prosecuting these & other issues. The risks & harms to humans, and even ecosystems, of loss of large predators may be minimal. Yet 'charismatic megafauna', black rhinos, pandas, whales, polar bears, have recieved among the most enthusiasm to save. Many want a world with wild, that these symbolise. But reintroduction of lynx, wolves, bears & wild boar, & even beavers, to areas that lost them is invariably problematic. Many farmers & rural people don't want actual wild, actual physical threats, or even just ecological change (beavers).
David Attenborough talked about the importance he felt of preserving parasitic wasp species. Their macabre life cycles make us feel a bit quesy. Sometimes they have an ecological role, preventing too large or concentrated a population of some prey. Ethically though, conserving them is conserving that prey-hosts suffering. Attenborough argues we need to value and conserve as much complexity & dynamism as we reasonably can, out of wonder, in humbleness, and for posterity.
It is hard to take any argument for preserving smallpox seriously, now eradicated in the wild. Or ebola. Or viruses and their biodiversity. Though, viruses may hold keys to understanding life, and recently gave us CRISPR/Cas9 gene editing technology.
A final point is, biodiverse ecologies are generally more resilient. Long term studies of grasslands show the more species, the better range of climate they thrive in. Beavers & many other ecological elements slow water through landscapes, reducing flooding and drought. Small wildfires are part of many ecologies, and prevent huge fires. Coastal wetlands may be able to produce more food than conventional farming, while feeding masses of wildlife: https://www.youtube.com/watch?v=4EUAMe2ixCI Climax ecologies often maximise biomass for minimum inputs, & do so resiliantly. We should learn from them, before they are all gone. Potato & banana narrowed-genepool monocultures further highlight systemic risks of losing wild crop ancestors & diversity.
Morality cannot be limited to considering only 'ground level' concerns. We must engage with what kind of world we hope for, wish to live in, make ourselves part of developing. Megafauna are majestic, though they may mean humans retreating from some landscapes. Ecologies are complex & sophisticated, our record of intentional interventions terrible, we must learn more, and that means conservation. Biophilia is the idea we are drawn towards environments with more varied and flamboyantly-present life in them. "Growth for the sake of growth is the ideology of the cancer cell." (Edward Abbey). Maybe biophilia is an alternative master-ethic to growth ('progress'), one that places humans at the centre, as gardeners of what could be a new Eden. But the knowledge to do that, is dissappearing with rapid climate change, and total human alteration of landscapes and ecosystems, just as we are truly developing the means to understand them. How we feel about causing extinctions, is a microcosm of how we feel about the choice to become a kind of plague, or a kind of angels. So far our plague-nature is winning.
Biodiverse habitats are generally more stable than less diverse habitats. For example, the arctic is commonly associated with sudden population explosions and die offs (lemmings, snowshoe hares, etc.). The implications for a world headed towards corporate agriculture and monoculture are pretty serious.
Biodiversity could therefore be considered essential to our security - one of the most prominent psychological needs. It could even become an issue of survival.
Many people also have an aesthetic appreciation of biodiversity.
In addition, the preservation of life forms requires the preservation of their habitat, yet another aesthetic quality.
There's probably lots of literature on the subject, though I'm not familiar offhand with any papers written by philosophers. On the other hand, many natural history authors can be quite philosophical in the broad sense of the term (e.g. Rachel Carson, Carl Sandburg).
You can check out the link below. Also, are you familiar with the concept of Gaia (the idea that Earth itself is a living organism, or something similar)? If not, that might be a good lead.
Biodiversity Preservation (Stanford Encyclopedia of Philosophy)
I might add that, for many people, the morality of not exterminating at least some species is intuitive. If it was suddenly revealed that elephants, giraffes or koalas were on the verge of extinction, there would probably be a global outcry for their protection.