Alexithymia is a term coined in 1972 to describe a condition where someone has trouble feeling or finds it impossible to express his emotions. While the term may be relatively new, the condition is not. Many times, people who can't express their emotions are assumed to have limited vocabularies or be shy, but often there are much deeper reasons.
Medical
Many times, the causes of alexithymia are not emotional at all and are medical in nature. The condition relates to the brain's chemistry and how sufferers process emotion. It is not the same as clinical depression, however, because the processing is a bit different.
Blocking Out
Blocking out can be done by either involuntarily forgetting a scarring memory or by intentionally suppressing emotions. In regard to the former, the mention and subsequent discussion of the blocked-out event isn't meant to give the appearance of cold-heartedness; it's simply that the person genuinely doesn't remember. Concerning suppression, a person will sometimes actually feel the expected emotion, but may be putting up a front for a variety of reasons.
Extraneous Empathy
Sometimes, only one or a handful of emotions is lost or not felt, not necessarily all of them. For example, the fear of confrontation can be a contributor to the behavior of those who never get angry. While a controlled temper is commendable, it is not normal to never get angry. Many times, the loss of emotion is simply a coping mechanism to compensate for some other distressing thing.
Domino Effect
After the coping effects of suppressing emotion have made their faux benefits evident to someone, the person can tend to then apply the method to other and eventually all emotions. It's a way that the person guarantees his safety and prevents himself from getting hurt. Essentially, it as an elaborate method of keeping one's guard up.