Equanimity is extremely important. Equanimity is a balancing agent to all the other Unselfish Emotions.
Equanimity helps balance and strengthen compassion. It is necessary because, without equanimity, when we open to Dukkha, we can become overwhelmed and fall into aversion or grief with it's existence. Equanimity strengthens the compassion so that we can to open to Dukkha without being overwhelmed by it.
In order to have Equanimity, we have to develop the wisdom to know what is our responsibility and what is not. By opening to Dukkha, we're not saying we have to take on the responsibility to end it in everybody else, because that's simply not our responsibility, and it's just not possible.
We learn this when we gain insight into the Four Noble Truths. We then understand: Dukkha exists, the true cause of Dukkha is ignorance, unwise reaction, and craving, and each person has to walk that path out of Dukkha within themselves. So this Equanimity that arises from this insight into the Four Noble Truths helps to balance our compassion, so that it doesn't fall into aversion or grief with the existence of Dukkha.
We develop a bigger mind that opens out to Dukkha, but doesn't get overwhelmed by it, because it understands that there are many things that are beyond our power of control. It allows more acceptance of Dukkha to arise, it strengthens our compassion, and it strengthens our capacity to open to the Truths of Existence. When we start to Universalize, that is to use the wisdom side of the practice, this helps to bring up both compassion and equanimity. We are then able to understand that it is impossible to change these Laws of Existence, and how universal they are, they do not just apply to ourselves, but to all beings. It's just a law. We can't change the nature of the cycle of birth and death. It is unsatisfactory, and we don't have the power to make the cycle of birth and death satisfactory.
So equanimity which is supported with wisdom, helps to keep our hearts open, protects the opening, allows us to care, but also to understand what to care about, what we can change and what we can not change.