As is probably obvious from the way I have phrased the questions, I believe genuine detachment does the latter in each case. It is possible to believe, using the common definition of the term, that detachment means an end to involvement, an end to relationships and to love, and even the loss of selfhood. It is possible, using this sense of the word, to set it in opposition to love and the involvement with others love demands, but in reality --- at least as I understand the term, and as the tradition of the desert Fathers and Mothers and other monastics and hermits I know understand it --- detachment is the means by which we are freed for authentic love; it is the matrix of Christian --- and so, eremitical --- love, not their antithesis. It is a mark and (partially) the means by which we claim TRUE selfhood, not the end or renunciation of it.
At the center of our understanding of the nature of detachment are a couple of truths: 1) we are called above all to love --- to love God and to love ourselves and others in, through and with God; this is the very nature of authentic selfhood, whether Divine or human selfhood, and 2) we cannot love God or others unless we have a self which is capable of this. Detachment, if it is a real value we pursue and cultivate must, like any other Christian value, contribute to these goals or it is worthless. More than worthless, it is destructive and even demonic --- that is, capable of distorting the persons we are and blocking the process of becoming God summons forth and grounds in us. But of course genuine detachment in the eremitical life, and in the Christian life more generally, is actually the basis for the freedom to be the selves we are called to be.
Detachment is the liberation experienced by one who truly loves and is truly human. It is, like so many other things in Christian life and spirituality, a paradoxical reality. If it is not marked by a rich and full loving, an abundant life of love and liberated selfhood, then it is not Christian detachment. And yet, how easily it is to fail to understand this! How common the misunderstanding of the term, even in those who are focused on spirituality in some way!
Detachment and the Creation of the Self capable of Love:
I wrote recently that real love requires distance as well as closeness, and that enmeshment was destructive of authentic human love. It is that insight that is at the root of understanding the nature of Christian detachment. There is a second and related insight which is also at the root of things here, namely, that real love requires freedom from counterfeits and a liberation from the concerns of an ego self which measures selfhood in terms of what we do, what we have, or what others think of us. This latter liberation is important not only to see and accept (i.e., love!) ourselves for who we really are, but to see and accept or affirm others (i.e., love them!) similarly. The choice before us is really to see and accept ourselves as God sees us, or to see and accept ourselves as the world (and our ego-self) sees us. There is no other option really. Detachment describes the state (and process) of moving from the latter to the former. It is a matter of freeing ourselves (or rather, allowing ourselves to be freed) from the claims and enmeshments (i.e., attachments) of the false self and embracing the true self and all that constitutes that.
But this goal is not an end in itself. Detachment is not something to be pursued for its own sake. Detachment is at the service of something greater in the Christian life. It is at the service of the true self, yes, but above all that means it is at the service of the call to that self to love as Christ loves. Our own truest selves are hampered from becoming or being embodied in many ways, but one of the most destructive is by the attachments we make and have to all those values, structures, and realities which support the "ego-self, " that is, the self which is constantly judging and composing a portrait of "Me" which, again, is defined in terms of what I do, what I have, and what others think of me. Not only is the ego-self noisy and constantly rehearsing this portrait of self in order to maintain it so that it blocks our ability to hear the call of our own hearts, but, because it is constituted by attachments to these things, it detracts and distracts from the complete dependence upon God and God's summons (vocation) which is the necessary response to it and the One who grounds and authors it.
Detachment is therefore the loosening and breaking of these bonds of attachment which are neither from nor of God, these definitions and images of self and others that hold us in their grip along with all that sustains and empowers them. It is a process and goal which again is at the service of a larger one, namely the making of authentic, obedient selves capable of loving others IN CHRIST. Communion is the fruit of detachment, and any supposedly "spiritual" process which does not lead to genuine communion should not be mistaken for detachment. The paradox involved here should be underscored: when we are truly detached we are capable of loving concrete human beings AS THEY ARE in our day-to-day dealings with them. Detachment does not issue in a merely abstract and superficial love of "the poor," "the homeless," "the unloved," or the like (Bondi, To Pray and to Love). It results instead in the capacity to see others --- real flesh-and-blood people with warts, body odor, lousy dispositions, contrary opinions, and the like --- and love them for who they REALLY are, namely, the images of God (as imperfectly as they -- or we -- realize this foundational identity!) who confront us with his presence everyday and who need to love and be loved in all the ways that we ourselves do and are called to do.
On Detachment and Apathy:
And this has implications for those who see detachment as a kind of apathy. As I noted in the beginning of this post, apathy is not the same thing the desert Fathers and Mothers called apatheia. Apatheia was understood to mean a kind of imperturbability or holy stillness which resulted when one was rooted in and lived from and for the love and mercy of God and was no longer enmeshed in the world. It was not only not incompatible with profound love for others, it called and prepared for it. Neither then is true detachment marked by apathy. Detachment and apatheia were intimately linked because both involved the freeing of the self from passions, that is from those distorting lenses formed by woundedness, neediness, insecurity, ambition, greed, etc, which caused one to relate to reality in ways which were less than authentically human. But detachment and apathy on the other hand are actually antithetical to one another because apathy is a form of self-centeredness and bondage resulting in psychological death, whereas detachment is a form of freedom from self which opens to life and love.
[By the way, please note well: the passions, in the sense this term is used by the desert Fathers and Mothers and those who have followed them, are not simply strong feelings; they may involve strong feelings but they are really distorting lenses through which we come to relate inappropriately or inadequately to God, ourselves, and others. For a very good treatment of the reality of the passions as understood by the early Church fathers and Mothers see Roberta Bondi's, To Pray and to Love. There she defines them as, "habits of seeing, feeling, thinking, and acting that characteristically blind us to who we ourselves, our neighbors, and God really are so that we are not able to respond appropriately, rationally, and lovingly." A longer treatment is found in her book, To Love as God Loves, also highly recommended.] Given this view of things what sometimes passes for detachment and is rightly described as apathy is actually what the desert Fathers and Mothers called a passion.
All of this leads back to the questions with which I opened the post. Detachment is a freeing process and state which allows us to love others more honestly and generously. It does not close us off from others --- even if we are hermits --- but instead allows us to see and cherish them with the eyes and heart of God. It allows us to delight in reality in a way which our ego-selves would censure and shut down, because the detached self, the true self, is unconcerned with what this reality can do for us, how it can be owned or possessed by us, or how it affirms us. Detachment makes us capable of delight in the thing itself simply because it is what it is. And, it allows us to hear and respond to the vocational call which sounds instant by instant deep in the core of our being. In other words, it serves authentic humanity; it serves the growth of the true self which loves God and claims as its own to cherish all that is cherished by Him. Further, while the eremitical life poses unique challenges in embodying this love, the FACT of it is no less real for the hermit than it is for any other Christian. For every Christian, including the hermit, detachment is the matrix out of which authentic love is birthed.