Suppose a species is brought to another region, where it quickly overruns its local rivals and drives the native species to extinction. This is something that has been suggested might happen with the larger grey squirrels that are slowly overwhelming the smaller red squirrels in Europe. Many people would suggest that this is a problem, but I wonder if that is really the case. One way or another, individual red squirrels will end up dying, either because other red squirrels are eating their food, or because grey squirrels are eating it. If more red squirrels die than would otherwise, the flip-side seems to be that there are more grey squirrels flourishing than otherwise. For the starving red squirrels, it doesn't seem to matter who is eating their food; and for the flourishing grey squirrels, it doesn't seem to matter where exactly they are flourishing. Of course, there is the risk of the newcomers ruining the entire local ecology and turning things into a barren wasteland, but that doesn't seem to...

You ask a fair question and I suspect that some of the answer, in the case of the squirrels, is that the red squirrels are thought to be more attractive than the grey squirrels, so many people would prefer that the grey squirrels do not take over. But there are also reasons for environmental concern (i.e. not just aesthetic preference) in that there is reasonable fear of a loss of genetic diversity and also fear of upsetting the ecological balance. Invasive species cause the extinction of other species without replacing them with other new species, hence loss of genetic diversity (and vulnerability to future environmental challenges). Invasive species also often upset the ecological balance e.g. rabbits in Australia and then cause the extinction of several species, not only the species that they directly compete with. Grey squirrels are thought to damage the woodlands in England, and thereby the environment of some bird species.