A father is father of his child. A brother is brother of his brother and sister. Well, then, Love is of something that it lacks. What is not beautiful or good, need not, therefore, be ugly or bad, just as there is a state of mind which is neither knowledge nor ignorance, but correct opinion. So Love is not a mortal, nor a god, since we have seen that he does not possess all beauty and goodness and happiness, which we must acknowledge the gods to possess, but is something intermediate, a daemon, interpreting between the divine and the human.
Love is one of many such intermediaries.
Your mistake was in taking Love to be not the lover, but the beloved. LOVE, you say, desires the possession of beautiful things. The happy are happy in the possession of good things. Everyone desires to possess good things. As for the phenomena of Love permeating all the living creation, they express the mortal nature seeking to become deathless by the one possible process of generation.