Thanks for your questions. I think they are important. I see them as especially important theologically, that is, in what we are saying about God in this assertion. When we suggest that God wants someone all for himself it gives us a picture of God that is distorted. While it is true that we are each called to live as someone belonging entirely to God, we must recognize that in Christian theology such belonging is part of giving our lives entirely for the sake of others. Both of these things are true at the same time. It is a significant paradox where one belongs entirely to God so that one may give oneself entirely to all that is precious to God. But this is not precisely the same, I don't think, as God wanting someone all for himself. That characterization of God sounds selfish to me; it seems terribly self-serving (both of God and of the hermit making the claim) and that is certainly not the God Jesus reveals to us.
Canon 603 defines this (solitary hermit) life as one of stricter separation from the world, assiduous prayer and penance, and the silence of solitude. Certainly, this is embraced so that God might be the One he has willed for eternity to be, and yes, it is for the hermit's essential well-being as imago dei. As such, the vocation is about union with God, no doubt. But the canon itself says it is not only for the praise of God but for the salvation of the world. In other words, we give ourselves entirely to God so that this relationship, 1) reveals the nature of God to others, and 2) is fruitful in the way any Christian vocation is meant to be. Eremitical life is not a selfish one and the God who calls one to this life is not a selfish God, but a God who gives himself exhaustively to us at every moment.
I can understand why you are having trouble arguing against this notion of God wanting someone for himself alone! I am also having trouble saying what is so profoundly disturbing about this notion (and it is disturbing enough to make me feel somewhat nauseous at the thought). It has, I think, something really fundamental, as one relative of mine might once have said, "ass-backward"!! Thinking back many years now, I have heard Sisters explaining their vocation to children by saying that God "wanted them for himself" as they talk about why they have embraced celibacy rather than marriage as they were consecrated to be the "Spouse of Christ". But while this explanation captures something of the special sense of being loved by God carried by the vocation, it is not accurate when taken at face value.This is because neither Jesus nor the One he called Abba want the Sister for themselves alone. God calls this Sister to this relationship because he wants the Sister's life for the sake of others and the missioning to others that being God's own allows and requires if God is truly to be Emmanuel!! We can reasonably talk about being God's own, for instance, and I have written here that we are called to our vocations for God's sake as well as for our own and for the sake of all we touch ministerially. I recognize that this is, to some extent, pretty provocative language, but I think it falls far short of suggesting that God calls persons to reclusive eremitical vocations because he wants them all for himself!! I suppose I just can't get other seriously flawed notions of God out of my mind here; this reminds me of child sacrifice or throwing people over parapets or into pits of flames, or cutting their hearts out as part of sacrificing them to a god who desires such things. It is an essentially pagan notion of God, barely one step removed from blood sacrifice made to satisfy the anger or blood lust of a tyrannical god.
I promise I will think about this more (in fact, I am likely not to be able to cease thinking about it!), and hopefully, I will be able to say more about what is wrong with this notion, or at least say it more coherently. As you capture in asking the question, there is something slippery about the assertion and we don't want to deny God anything God truly wills or desires. But the idea that God could want someone just for himself alone is perverse when we are dealing with the God of Jesus Christ who reveals himself as self-emptying love-in-act. After all, God is not a human person-writ-large nor does he need or desire us in the way other human beings need or desire one another. He is "Wholly Other" and yet loves us exhaustively so that he (and we) may be given to (love and serve) others in a similarly exhaustive way.