Non-attachment does not mean that you do not care. Non-attachment means that you do not grasp. We have a tendency to grasp at and then stick to everything we come in contact with, through hearing, tasting, seeing, touching, smelling and thinking. This grasping is at the root of much suffering. Let's imagine that I am holding an object made of gold. It is so precious and it is mine - I feel I must hold onto it. I grasp it, curling my fingers so as not to drop it, so that nobody can take it away from me. What happens after a while? Not only do my hand and arm get cramped but also I cannot use my hand for anything else. When you grip something, you create tension and you limit yourself.
Dropping the golden object is not the solution. Non-attachment means learning to relax, to uncurl the fingers and gently open the hand. When my hand is wide open and there is no tension, the precious object can rest lightly on my palm. I can still value the object and take care of it; I can put it down and pick it up; I can use my hand for doing something else. If you do not uncurl the fingers, your holding becomes one with what is being grasped and you are taken over by it. You see the precious object outside its context; you are blinded to other possibilities and reduced to what you are holding. Non-attachment is part and parcel of equanimity and leads to a more spacious approach to life. Non-attachment is not indifference but, on the contrary, leads to true caring and compassion. If a mother hugs her baby too tightly, the baby will feel uncomfortable and cry. But if she holds her baby too loosely, the child is likely to fall. So the mother must hold her baby just so, not too tightly and not too loosely.
Martine Batchelor (in Meditation for Life)