I agree that overpopulation is a serious issue that needs to be dealt with. But why is killing people the way to do this?
This is generally the way population geography works: You'll typically see that as death rates rise in most places, so do birth rates. This is because the more people you see dying of causes other than old age, the more kids you're going to have, to ensure that at least some of them make it to childbearing age. This effect often more than offsets its cause -- when the death rate jumps, the birthrate will jump several fold higher, and will often take a while to come down, even after the death rate drops and pretty much everyone starts living long enough to have their own kids.
So what do we need? We need below-replacement-level fertility. Only one, with a wince I say MAX two, kids per woman, across the earth.
The only statistic that consistently correlates with lowered birthrates is the rate of female education. In places where almost all women have completed the society's most basic level of education needed for most jobs, you see below-replacement-level fertility. No other incentive, disincentive, plan, or policy has succeeded in producing this effect. It probably isn't hard to see why. If women CAN work, many WILL work. Working women have an avenue for existential fulfillment besides motherhood, and just won't likely have the time or energy to raise more than one or two kids. If they live in a city, like most people in low-birthrate countries do, then nor will they have the SPACE to raise more than one or two.
If every woman had a maximum of one child, the world population would halve in a 2~3 generations. The only way this will be achieved is by equitable educational opportunities for all people, but especially all girls, across the world. This is why I believe in poverty eradication and education oriented causes, as a balm for the world.
I also believe in finding a way to close income distribution gaps. High GINI coefficients (a measure of inequality) correlate strongly with violent crime rates, which obviously push up death rates, and therefore birthrates, among affected populations. This is because when people see what others have and have far less, this makes enough of them willing to resort to violent means to get what they're jealous of.
There now. A plan to combat overpopulation, without a single untimely death. Enact this plan, and there'll be plenty of resources left to care lovingly for that quadrapleigic AIDS patient on a ventilator.