Its a spiritual problem and the person asking doesn't really know who God is.
A few times some of the mystics used metaphors to describe their ecstasies that might be taken by some people too literally, something they never intended.
However people sometimes confuse God's sort of love called
agape, and eros which is the love between the sexes.
Eros when it meant spiritually is about climbing, assent, climbing up to God, however God in the Bible is one who descends to us. Eros and Agape therefore are not the same. Eros it has also been said is more godlike than the other loves such as friendship and family love, it is also more prone to become a 'demon' so to speak, when worshipped, so the answer is no, eros is possesive not self-giving in the way that
agape is.
God is love, but his love is "more stern and splendid than mere kindness" it has been said. Firstly its a self-giving love between God the Father and God the Son that has always been from before Creation. There was love and communication on the high order of Trinity before time.
A misunderstanding might occur in regard to 'self-giving' - its not 'throwing oneself away' in a careless, or worthless manner, to be taken advantage of - that's nothing like what it means at all, just for clarity.
Augustine also of spoke of
caritas (latin), meaning sharing within the christian commonwealth.
http://faculty.goucher.edu/eng330/caritas_vs_cupiditas.htm
It takes God's agape which comes to us through Jesus Christ to set our human loves in order. Dante said this long ago: "Set love in order, Thou who lovest me."