Derrida doesn't (or so I'm told) share my Christian faith, though that's more something for God to sort out than for me to presume to do. His focus on the curious tension between "who" and "what" when it comes to human love is very pertinent regardless. And in fact, he doesn't rule out love also being for sub-human or super-human beings.
I wonder, and this is a very unfinished thought which others may have pursued centuries before my birth, if loving a human being's "who" and "what" is aided by a common love for something or someone else which both lover and beloved share.
Yes, I'm talking about God. Of course I am. I do not always speak bluntly on such matters, but when it comes to love -- which I admit is transparently the thing I most hunger for -- Jesus Christ's absolutely unique Personhood is my only resolving factor. Agape, or "disinterested love" (a love not rooted in "getting" or "having" but rather in simply "being"), is uniquely expressed in the Jesus story.
That love colors my love for my wife Carol. And it colors our love completely. In fact, I have had a few rather mystical moments in which my love for Carol suddenly was revealed as being my love for Christ who lives in her, and who in an almost tangible way, is her. Some of these moments came in one anothers' arms, but more of them came in everyday moments when I was surreptitiously watching her without her knowledge. Suddenly, Christ and Carol became indistinguishable. (No, I'm not a pantheist, and I think Scripture itself is fairly strong on this idea... perhaps I'll defend it via the bible another day.)
For now, I offer Mr. Derrida's rather tentative reaction to being asked about love as something which might cause each of us -- as humans, as Christians, and hopefully as both -- to ponder love and our own reasons for loving. And I suggest that Mr. Derrida may be skillfully playing with us (he loves the concept of play) with his dichotomy between "who" and "what," which after all is in the deepest sense of things a false dichotomy. I love God... because God is love. Do I love Him because he is "God" (Who) or Love (What)? No, I love Him only and because he is both God and Love. While "who" and "what" may work on the superficial level of "Carol" vs "Carol's deep brown eyes" (I love them both, but if she was blue-eyed I'd still love her for being her), "who" and "what" on the deepest level of reality cease being a dichotomy and meld into one, One Who has always been both.