The love of God is often thought of as being similar to parental love, but no metaphor is perfect.
Parental love is not a free choice. Deeply embedded biological programming, powerful hormones, and the subconscious communication of our limbic systems drives us toward affection for our offspring. And parental love is not only biologically conditioned it is a social obligation.
By contrast, God has no biological or social imperative for loving us. God does not love out of any obligation, but for the pure joy of it. In this way God’s love is not parental. There is another metaphor which better conveys what God’s love is like: geeky.