If attachment is a cause of suffering (through grasping) then detachment is also a cause of suffering (through aversion). Clearly, detachment from experience cannot be our aim. Instead, we look for the space between dualistic opposites because that is where we find freedom. In this case, the space that liberates us from attachment and detachment must be non-attachment to arising experience.
Non-attachment is equanimity, a state of being which develops when we fully understand impermanence. We can cultivate equanimity (upekkha) as a practice; it is one of the sublime abodes of Brahma-vihara. But it is also a fruit of insight into impermanence.
Non-attachment is characterized by unshakable stability of mind that neither clings to nor rejects experience. If a mind is truly non-attached, compassion, gladness and kindness will not be far away, like the interconnected rooms of a house. If detachment is present, it can be recognized by a quality of standing away from experience, a kind of aloof response to what is happening. However faint, this is still aversion. Finally, indifference may masquerade as equanimity, but it can be known by the fact that compassion and kindness are absent.