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.
People usually cling to things like those burdock burrs that children throw at each other's clothes.
By doing this, you limit yourself. You reduce yourself to what you are grasping – being like this, having that problem, being affected by this painful word or that unpleasant experience.
This process does not need to happen. Non-attachment can help you dissolve the patterns of grasping.