Both of the existing answers are good, but a glimpse of the chemistry behind the answers may be helpful.
There are four elements which are critical for life:
earth, air, fire Hydrogen, Carbon, Nitrogen and Oxygen -- H, C, N and O. (There are others such as calcium, sodium, potassium, iron and sulfur needed also, but in comparatively trace amounts.) Carbohydrates, starches, sugars and the like are basically polymers of CH2O. Proteins are polymers of amino acids which have the general structure NH3CHRCOOH, where R is a add-on usually made of C, H and O.
Diamond is pure C. No matter what you do to it, you can't make any of the inputs for life without adding O, H and N. So with diamond but without a supply of volatiles also, you'd be dead. (Rich, perhaps, but dead.)
At our favored temperatures, most compounds of O, H, and N are gases or liquids, and gases and liquids go by the generic name of "volatiles". (There are also some very common carbon compounds which are common volatiles in space: carbon monoxide, carbon dioxide and methane are the most common.)
(I'm actually puzzled that they care about diamond, since it's not a particularly useful form of carbon and carbon is pretty common, anyway. But as a source of carbon, it's pretty sexy.)
Because the volatiles are, well, volatile, they tend to escape during planetary formation, and the smaller the planet the less able it is to hold onto volatiles. Smaller inner Solar System bodies like meteors and asteroids tend to be high in non-volatiles (iron, silica, carbon) and low in volatiles. Most plans for permanent settlements in space are focused on finding in situ sources of volatiles. (Consider the discussions of bases at the Lunar South Pole, which is believed to have deposits of water ice.)
So, bottom line, volatiles are expected to be the limiting resource pretty much anywhere in space where humans can survive.