The standard '
Scientific' explanation is that the
carbon-carbon bonds in diamond are too stable, no
enzyme would be able to overcome the
energy barrier necessary to disassemble diamond.
However, diamond is something of a special case for carbon compounds (oh, fullerenes are probably pretty inedible). There are organisms that 'eat' rocks, reduce gold salts to elemental gold and other improbable diets (from the point of veiw of sugar-eaters). There are bacteria that derive energy from sodium and some that produce hydrogen or eat methane. Many organisms can synthesise silica polymers - and I don't in principle see why you couldn't engineer bacteria to make silicon chips.
The message is that it's more surprising what Life can do than what it can't.