None. No importance what so ever. The ego is what is looking for “shoulds” and “should nots” and rank by importance and trying to do something (like – not being attached).
It is true that the enlightened are not attached to things and people. When there is a seeing through the illusion of “me”, the illusion of attachment also falls away as it is founded upon an illusory “me”. However, there is no such thing as “the importance of not being attached”. There is no need to try to not be attached. In fact, the enlightened don’t really think about attachment or detachment.
What is attachment? Really, it is mental grasping and clinging. It is a trying to hold onto or possess. There are two main pins that hold this facade up: denying impermanence/change and believing in a “me”/”otherness”.
Firstly, we only try to hold on because we think we can hold on. However, all things change and are impermanent. You are not able to hold on…never could. You may buy a new coat that you saw and loved, and then later that week visit some friends who have cats. While visiting, the cats shred your new coat. You were going to be parted from the coat at some point…sooner or later…and this time it was sooner. You just don’t know when things or people will leave your life. All things come and go. Resisting this (mentally grasping/clinging) will not make them remain a minute longer in your life. You just don’t control when and how things will leave your life.
And second, there has to be a “me” to claim possession. There is no “mine” or “my” without a “me”. There has to be a “me” to try to resist change…a “me” that wants something other than what is. There has to be a “me” trying to hold on. These are stories we tell ourselves. We own nothing in this world…”my” and “mine” are illusions. We can’t really hold onto something that is leaving or has left. Attachment is not physical…it is purely mental (and based on the beliefs and stories we tell – emotional as well).
Attachment causes suffering. We fear that the thing/person will leave our lives, try to hold on, vexed when we find we can’t hold on, and grieved when it does indeed leave our lives (as it always would at some point – or you would have to leave it). So not being attached sounds great to some egos. People then try to not be attached and fight against their attachments. This, of course, does not do anything to delve into this “me” that has attachments and wants to be detached. Seeing through the “me” is key. All else is really a distraction.
If you are going to distract yourself, don’t try to work on individual attachments or try to detach from specific things. Investigate and delve into the idea of attachment itself. If you clearly see the futility of trying to hold onto that which is impermanent and changing (and accept impermanence and change), then you might find that you automatically cease trying to hold on. We typically do not do things we know are futile. Only when we have a hope that it might work (still ignorant of the futility), do we continue doing something that is futile.
This distraction would be missing the deeper root of a “me”, but at least you are going to a root belief that you could hold on. This is more effective than working on individual attachments. It would be better yet to go to the root…the “me”.
As I said, the enlightened are not attached to things and people. So often the follow-up question is “do awakened people not grieve at the loss of loved ones?” I would say that typically the answer is no, but not absolutely. The danger of such questions is that people are looking for “shoulds” and “should nots” and absolute standards to measure by. “Oh, you cried at your mother’s death…so you must not be awakened.” I would never say that. However, I know of no awakened person who for weeks later still cried, fell into depression, or otherwise was attached to a body/mind that no longer is.
Why cry? It could be because others around them expected it. I heard of an awakened one who started out not crying at a funeral for a loved one, someone asked him why wasn’t he sad, and then he started crying. Some may cry before being asked because it is the thing expected of you by others. Some may cry from some emotion. Not out of a personal loss of some kind, but like how we might cry while watching a movie when a character we have come to love, respect, or otherwise honor dies in the movie. Or how some people might cry when a great actor has finished their part and leaves the stage. It is an acknowledgement of the part they played. There could even be tears of joy…why assume the tears are from sadness, grief, and loss? There could be joy in knowing them or having them in your life for as long as you did. There could be joy in knowing the deceased has returned home (so to speak).
Ultimately, there is no winning or losing…no gain or loss. We never lose loved ones…because we never had them (we can’t possess even ourselves). In the constant change and flux of the world, their time in your life was over. I see no point in grieving the passing of people (loved ones or not) or things. Instead I see joy in that I ever knew them at all and they were in my life for as long as they were. There is gratitude and appreciation…not grief and sadness.