I love how people think the world is getting overpopulated when all of the world can fit into the USA with plenty of land to spare.
And there is more to the dang world than america.
Also, cancer is not in anyway natural. It is caused by mutations.
Humans are small and the earth is very very big.
Space for habitation isn't a limiting factor on human population, atleast not on earth. You'd need unimaginable numbers of humans to run out of space.
The limiting factor for a large population on the earth is more to do with resources, but even at this moment of time, while we may worry that there aren't enough fossil fuels to provide for all of Earth, there really isn't much concern for overpopulation at this time.
Since fossil fuels aren't a food source or something similar, and instead are only used for heat and electricity, so long as we can find better alternatives (and start using them en masse), then we'll be around that limitation.
And an increasing population would, if anything, drive the world to seek for more renewable energy sources, such as solar, wind and tidal energy, and even nuclear.
Killing people off to solve this one problem with population wouldn't help. It would slightly slow it down, perhaps, but the world will adapt around it (and almost certainly for the better), so killing people off would slow down this journey to the next advancement in energy production.