Theresa said:A sixth misunderstanding about love is the idea that God is love is unrelated to dogmatic theology, especially to the doctrine of the Trinity. Everyone can agree that God is love, it seems, but the Trinity is a tangled dogma for an esoteric elite, isn't it? No. If God is not a Trinity, God is not love. For love requires three things: a lover, a beloved, and a relationship between them. If God were only one person, he could be a lover, but not love itself. The Father loves the Son and the Son loves the Father, and the Spirit is the love proceeding from both, from all eternity. If that were not so, then God would need us, would be incomplete without us, without someone to love
I'm afraid the whole problem is from here. This is a good and well-known explanation but it is only explanation, it can't be used to proof any doctrine. That passage say "Love exists between two persons, therefore the Spirit proceeds from both the Father and the Son" but we shouldn't apply our understanding of love to God. The Trinity is revelation, not logical development of the idea of God. St Gregory the Theologian in the end of his Homilies on Theology (c. 380 AD) warns that any analogy is limited and can be dangerous if we will derive our view on God from it.
Also the Orthodox Church teaches about distinction between essence and energies of God, which is rejected by the Catholic Church. Love is an energy of God, it is how He reveals Himself to us. It is not about His inner being.
I apologize if I explained not very clear, hope the other will add to this.
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