I don't think it's purely rational. It's probably the case that loss aversion[0] or some combination of psychological phenomena play a huge role. But I suppose the rational component is: If it's practical to save a species, and that species may provide some useful knowledge or inspiration in the future, why not save it?

> If more species is best, should we bread or genetically engineer new ones? Is that “better”?

I get what you're saying, but you have to draw the line somewhere. For example, if more money is better, why not work 3 jobs?

[0] https://en.wikipedia.org/wiki/Loss_aversion