This is absolutely not true. Diamonds are not common. And diamonds are not so easily made. They can be made either by the High Pressure High Temperature (HPHT) method or by Chemical Vapour Deposition (CVT), and for you to have a really high quality diamond is not really easy. Most of the diamond production in the world ends up going to drills and scientific purposes, such as lasers and other assorted uses. As of 2013, some 2% of the gemstone market was comprised of artificial diamonds. And yes, as sunnyj.allday has written, market prices are not necessarily correlated to something's rarity. Still, natural diamonds are not common.

Diamonds are expensive because people perceive them to be expensive and it all started with an ad back in 1947 for De Beers engagement ad campaign. "Diamonds are forever." In all reality its just a common rock.