Future generations (persons who are not present today, not even born or conceived) are going to be affected, positively and negatively, by what present generations do.
Effects on future generations are often ignored when decisions about large-scale resource policies and about far-reaching technologies are made. Future discount rates used in economic planning effectively forbid planners from taking much notice of costs and benefits to be felt no more than thirty or fifty years in the future. This is now an anachronism, because it has become quite evident that technologies and environmental activities have reached a point where they have much more far-reaching effects on the future than before.
Whatever is right for our grand-children is always uneconomic and almost always impolitical.
"Future generations are unlikely to condone our lack of prudent concern for the integrity of the natural world that supports life". (Rachel Carson, 1962, Silent Spring).
Is it fair to leave for a population that will inevitably be much larger (whatever to be much better off) a natural resource base that has been depleted and rendered significantly less productive than it is today?
Why do we care about the future? Our progeny. What are we trying to "sustain"? A healthy habitat 'primarily for them'. If we sought a sustainable habitat for various chemical eating microbes, diverse organisms and plants that thrive on our waste/pollution, we would happily continue our current behaviour. Shrinking biodiversity and killing off many species in our food chain will improve the sustainability for the remaining life forms better adapted to the altered environment.
The progress that humanity has experienced during the last two centuries has no precedent. Pessimistic forecasts about human prospects have been repudiated by the reality of material progress. The record of humanity shows that, on average, the people in each generation have created more than they used. This must be true to account for the increase in wealth of numbers of human beings. If it were not true, we would have become extinct.