Equanimity is also the seventh Factor of Enlightenment. Equanimity, as a Brahma Vihara, as an Unselfish Emotion, means we have Equanimity towards beings, and this is not the same as Equanimity as a Parami, nor is it the same as Equanimity as one of the Seven Factors of Enlightenment. There is a difference. Equanimity, as an Unselfish Emotion, is just directed towards beings. Equanimity as a Parami or as a Factor of Enlightenment, is a higher Equanimity. It not only includes Equanimity towards beings, but also Equanimity directed towards the Three Characteristics of Existence. This is the basic difference between Equanimity as a Brahma Vihara, and Equanimity as a Parami or Equanimity as the seventh Factor of Enlightenment.
The Equanimity of the Paramis or the seventh Factor of Enlightenment concerns the impersonal nature of existence. It's sometimes very difficult to say to the Dukkha arising coming from the Three Characteristics that, "They are the owner of their own Kamma". So we need to get a deeper insight into Truth on a higher level. But in order to be able to do this, we have to develop the emotional maturity of Equanimity as a Brahma Vihara, because unless we are emotionally mature, we are not able to deal effectively with deeper insights. They can then unbalance the mind too much, because too much of our happiness and security is bound up with worldly happiness.
What the Brahma Viharas help us to see, on an emotional level, is that happiness comes from within ourselves. It comes from lessening the sense of me, and becoming unselfish in our emotions, that is lessening selfishness. Then we are able to see that we don't really have so much to lose by becoming unselfish and lessening the sense of me. And on a higher level, as we start to see the impersonal nature of existence, of this Law of Cause and Effect and how impersonal it is, this can be unsettling to the mind, if people are very attached to themselves as a solid static entity. But, in reality, the self is more like the Mississippi River. It exits, it's in the United States, but if you go to Mississippi River, and stay at one side of the Mississippi River, and look at one spot of the Mississippi River, is it the same water going by? We see it's never the same water, but rather it's constantly changing. Just as it is with ourselves, this concept "me" remains the same, but what it's describing is constantly changing.