Overpopulation.

There are over six billion people in the world.  Why are people so adament on saving as many human lives as possible?

There is amibiguity over the word "overconsumption". At this point in time the countries with the lowest (and stable or declining) population densities are the ones doing the most consuming. Most would classify such countries as "overconsuming", and say that all other countries are either consuming at a safe level or underconsuming. 

Overpopulation is not terminology wisely used to make a global reference. We simply do not have enough knowledge about the biosphere to come to any conclusion that we are coming to or crossing a threshold where the Earth can longer sustain the same human activity that has been going on for the past 200 years. A LOT of assumptions have to made. To make these assumptions and suppose a plan of action based on them is conjecture. 

I would say overpopulation is defined as the inability of that population to support everyone at at least a certain living standard. This does not preclude a lack of resources (overpopulated countries tend to be poor, poor countries tend to be underconsuming). It can mean the lack of means to harvest and exploit said resources. I would say in practically all developing countries this is the case. The answer to overpopulation in these areas is then economic development.