This is a funny one, because the word, "emotion," we generally think there is feeling with it. A feeling, an emotion, anger, or something. We tend to think of it as something that can be physically seen or at least identified with. We have love, we have sympathetic joy, we have anger, we have all these things which we normally call feeling or emotion in English. We generally think that there is a physical response to a feeling or emotion.
However, with Equanimity there is not much emotion on a physical level. But that is just what it is, that is Equanimity. The lack of excited emotion. So try to think of it more in that way, there is still kind of an emotion involved, it is just not an excited emotion. Maybe when they define an emotion, maybe they would say Equanimity is not one. Within Buddhism we are going to say it is one, but it is one of the Unselfish Emotions. Now one of the reasons it is with Compassion, Lovingkindness and Sympathetic Joy, is that Equanimity is of great importance for our development of Compassion, Lovingkindness and Sympathetic Joy. It has to be there, it is part of them. If we don't have Equanimity with our other emotions, then the emotions go off balance. Compassion can easily go into anger on one side, grief on the other. So the Equanimity is actually a balancing agent for the other three Unselfish Emotions. So looking at Equanimity, from a slightly different way as to being an emotion without a strong physical expression of emotion, but as a very important aspect of the Unselfish Emotions because it absolutely has to be there to balance and support the other unselfish emotions and to make them stronger.