There are people who believe emotions are unnecessary and so seek to distance themselves from their emotional experiences. There's certainly nothing wrong with gaining some distance from our emotions. In fact, it's a skill we need if we want to function "normally" in society. Distancing ourselves from our emotions is only problematic when it becomes our primary method of responding to our feelings. The eventual result of suppressing every strong emotion that arises is emotional detachment. To be emotionally detached is to no longer recognize the physiological changes that accompany each emotion. These changes continue to occur, they just do so outside of conscious awareness.
At its core, emotional detachment is nothing more than the absence of self awareness. There are, of course, some who say that ignorance is bliss; you cannot feel pain if you cannot (or do not allow yourself to) feel. In my opinion, a life devoid of emotion is an empty life indeed. I cannot imagine living a life without happiness or a life without love. It is difficult to think one could find meaning in such a life. And yet, there are those who choose this path; they give up the pursuit of happiness in an effort to avoid pain.
It doesn't work. In reality, refusing to engage with our emotions has consequences that go beyond missing out on the richness of emotional experience. It turns out that actively suppressing emotions impacts our physical health as well. Several studies have shown that suppressing emotions (both negative and positive) leads to increased sympathetic activation of the cardiovascular system. When the cardiovascular system is hyper-activated repeatedly over an extended period of time, "such...activation might lead to chronic functional and structural changes of the cardiovascular system that compromise its performance" (Mauss and Gross, from Chapter 4 of "Emotional Epxression and Health: Advances in theory, assessment, and clinical applications," 2004). Related health problems include hypertension and atherosclerosis, both of which lead to an increased risk of heart attack and "sudden cardiac death."
Simply stated, chornic emotional suppression is bad for your heart. Or, as I frequently caution my patients: "If you don't deal with your emotions then your emotions will deal with you."