One thing to think about is the assumption that extinctions caused by humans are necessarily a bad thing. Nature tends toward equilibrium, true, but it is not always the same equilibrium. An ecosystem that is stable can have a superior predator move into the area, and it will be changed as certain prey die out, and maybe even some predators will die from lack of food. Nevertheless, stability will return to the environment.
There are basically two ways of thinking about humankind; that we are advanced animals and part of the world ecosystem, or that we are a superior and separate type of being and merely living among animals.
For the first school of thought, the argument that we are intruding and ruining an ecosystem is ludicrous. We are part of the world ecosystem; it is evolution in action if the inferior animals cannot compete. We are intelligent enough to decide if we want to keep them around for a specific purpose, but characterizing their extinction as immoral is hypocritical.
If you think of humans are a separate, higher form of being then you probably don’t have any problem with the extinction of species. If you do, ask yourself why. Animals die all the time, for various different reasons. Most of them have to do with their inability to cope with the environment, be it a fast animal with big teeth or an SUV with large tires. Why should we care if it is a certain type of animal that is dying rather than a different type?