Why did the military choose .308 for its precision rifles in the past and now?

I know this will probably bring up arguments of how the .30-06 is better and the .270 is almost the same... blah.. blah...blah. We've all heard that and read it multiple times by now. My question is, why did the military decide to use the .308 or 7.62 NATO as its basic precision rifle round? Why not the .30-06? Or the .270? Both were around longer and before the creation of the .308. Why not a a bigger round? Any ideas? What does the .308 have that the .270 or .30-06 not have?