Our nature must be selfish

If the issue is individual survival, then it's no surprise that the behavior needs to be selfish. If selection is correlated with each individual's survival, then our nature must be selfish. 

What the Bible says is consider your collective effect on your environment. Once you can begin as a collective to cultivate your environment and create abundance it will also enable you, nay it will compel you, to exhaust your environment and  to undermine that abundance. Then your survival will return to the laws of the jungle where it will depend not so much on your being able individually to out-compete your rivals as it will depend on your being able to co-operate with your rivals to sustain your environment; and while that might not be congenitally sensible to you it could well be culturally sensible to you. 

The impulse to survive can also be achieved by eliminating one's rivals. That situates the notion of survival of the fittest in an entirely different light. Then natural selection becomes an offshoot of unrestrained sexual selection.