We all know that it is better to give than to receive, and Deus Caritas Est doesn't deny this. But it does emphasize that the giving of love must not supersede the reception of love as well, since we all receive love from God without any hope of ever making adequate return.
8. ...Anyone who wishes to give love must also receive love as a gift. Certainly, as the Lord tells us, one can become a source from which rivers of living water flow (cf. Jn 7:37-38). Yet to become such a source one must constantly drink anew from the original source, which is Jesus Christ, from who pierced heart flows the love of God (cf. Jn 19:34).
This immediately put me in mind of two fictional characters: Mrs. Fidget from The Four Loves (fresh in my mind) and Lady Marchmain of Brideshead Revisisted. Both are emblematic of a suffocating kind of love which only wants to give and never receive. Mrs. Fidget is a bit of a caricature, of course, since Lewis created her to illustrate a point. But the caricature contains a great deal of truth. Mrs. Fidget is, in her own estimation, a long-suffering woman who gives and gives to her family and is never truly appreciated. The problem is that her giving is shallow and self-centered, since it doesn't have anything do with what her family actually needs. She constantly demands affection, yet rejects it when it is given her. To open herself enough to really receive love would demolish her fantasy world of resentment as well as her created identity as the one who gives but never receives (as if receiving love were a fatal weakness).
Lady Marchmain is a far more complex character. She truly believes that she is doing the best thing for her increasingly alcoholic son Sebastian, first by creating a bond of obligation through her financial assistance and influence on his behalf, and then, when he rejects these, by her constant suffocating vigilance. Her actions are externally correct, most of the time, and her intentions are good. But her attempts to shelter him from the consequences of his actions (or from committing actions that have consequences) backfires because they stem from a wrong conception of love as always giving and suffering. She would indeed be happy to receive love from Sebastian, but it must be love on her terms and under her conditions.
It is not that one must receive love when one gives; many saints labored unappreciated and unrewarded in their earthly lives. But the self-donation of giving love must also extend to being open to receiving love, even if it is not love as one expects it. Loving your neighbor as yourself means not only giving love to him as we do to ourselves, but being as willing to receive love from him as we are to receive it from God.