We see that outcome all the time. For example, there is global interest in saving the gorilla from extinction, and lands set aside for them. Food is food, and a few well-aimed guns can scare off legions of conservationists who stand between a man and a family meal. Americans are little different, and will allow richly diverse forests to be felled for grazing land so they can toss a juicy steak on the grill. Or, more subtly, conservation areas have been flooded by the construction of dams meant to provide water to urban populations.
Priorities can change as populations grow.
In the time it takes me to teach my 10-week course on human ecology, the human population of the world grows by a number greater than the count of people in my home state, Ohio. Those new people need sustenance. What they take is largely a matter of space, but water and other resources are also drained away for our own purposes. The result is extinction of other plants and animals that need the same things. People may not get excited about the loss of a rare nematode, but they might sit up and listen if they know that extinctions threaten their very livelihood.