I have been shooting the .308 Winchester for years! For an all around deer caliber, the .308 takes a back seat to no one!
As others have said there are many good calibers that will suit your purposes. The .308 is as good or better than any of them!
The pluses are : it has been around a long time and is well proven.
While guns will vary, the .308 caliber is a very accurate caliber.
It is a top ten seller, so ammo is available anywhere and being a military caliber there is always a lots of cheap surpluss ammo for practicing.
The .308 within reasonable ranges is capable of taking larger game than just deer.
It does all this and more, with managable recoil.
So, to each their own, but you cannot go wrong with the .308 Winchester!