Balancing Compassion and Equanimity is about opening to the humanness of a situation and understanding that we do not have the power to change the characteristics of existence. Understanding our limited power helps us to develop more equanimity, "to care and into not to care". I often bring examples from nature to help in these situations, one example is about perfect seeds. We have perfect seeds to make the world beautiful, to have peace and happiness in this world.
So from special beautiful flowers, we collect the perfect seeds to make the world beautiful. Then we throw them out into the wind. The wind catches them and blows them away and we think it is wonderful, we are going to make the world beautiful. After a while we think, "I wonder how my flowers are doing?" So we go and see a plant over there with beautiful flowers all over it, "Oh, this is a perfect thing. It is a perfect plant and it has perfect flowers." But then we have a closer look and see that the soil is very good quality. All the other plants around are healthy, as well. We see it must get enough rain, just enough sun, not too much afternoon sun, "Ah well, it is a perfect seed."
Then we go looking for another one and we spot another plant, but it is not as big as the other one and the flowers aren't that big either. We look closely and see the soil is not as good. All the other plants around look a bit like that, too. It must not get enough rain. And look at that western sun, "Oh, well, but it was a perfect seed. It should have been able to overcome all those conditions. It was a perfect seed!"
Then we go looking for another one and we see one, "Hey, this is much smaller, what happened to you?" You look at it and the soil is like sand and all the other plants around look a bit sad, too. We see it doesn't get enough rain and sun is beating down on it, it is hot. Even though it is a perfect seed, it depends on other things, doesn't it?
Then you go look for another one and we see a seed on cement and the ants are eating it. It never had a chance to grow at all. And we realize that there are many things beyond our power to control in this world and that it is important to us to develop equanimity and understand this certain lack of power over the Three Characteristics of Existence: impermanence, Dukkha and "Anatta," not self, not me, not mine.
Understanding the third characteristic is quite important for developing this balance. Another example I give is suppose a person comes to me in the interview and they tell me their problems and I have compassion for them. (And you can project this into a friend coming to see you as well.) I listen carefully and I see the problems arise because they don't accept that things are impermanent in this life. So I try to explain this to them and say, "What would be helpful is that you reflect on impermanence and understand that things arise and pass and we can't change this."
They may respond with "Impermanence? I don't want to reflect on impermanence!" And then they go away. They come back later and they tell me their problems again and I feel with them and I say, "Well, it seems like you still have some trouble with this impermanence." "Impermanence? Can't you give me something else? I don't want to reflect on impermanence!" "But you see the problem is arising because you don't understand the impermanence of things." "Oh well, I'll try." And they go away.
They come back later and they tell me the same thing. After a while I realize I really can't help this person. So I have to have equanimity towards this person, because it is not possible for me to change the nature of existence to make impermanent things permanent to make them happy. If we understand that we are not in control of the causes for their Dukkha, we are also not in control of the ending of it either. And that helps to develop more equanimity towards these situations.
Perhaps there have been times in your own experience when you tried to help someone, perhaps you explained some good techniques but they didn't follow your advice because they won't accept the Three Characteristics of Existence being that all things are impermanent, there is Dukkha and that nothing is really ours. It is not within our power to change these characteristics of existence
If this person is unwilling to open to the nature of existence and is blaming others for their suffering, then it is very difficult to help them. It is not possible for us to change others to meet their expectations to make them happy, that is impossible. This is why it is very important for us to develop compassion balanced with equanimity so that we know when to care and when not to care.