Love is not merely a characteristic of God. God is not merely loving. On my best days I am loving.
But Scripture makes the profound claim that, “God is love.” Love is who God is.
This is why the Trinity is the central mystery of Christianity.
God is Lover. God is Beloved. God is Love Exchanged.
God is Trinity because God is Love.
“In the course of its history, Israel was able to discover that God had only one reason to reveal himself to them, a single motive for choosing them from among all peoples as his special possession: his sheer gratuitous love.
“God's love for Israel is compared to a father's love for his son. His love for his people is stronger than a mother's for her children. God loves his people more than a bridegroom his beloved; his love will be victorious over even the worst infidelities and will extend to his most precious gift: ‘God so loved the world that he gave his only Son.’
“God's love is ‘everlasting’: ‘For the mountains may depart and the hills be removed, but my steadfast love shall not depart from you.’ Through Jeremiah, God declares to his people, ‘I have loved you with an everlasting love; therefore I have continued my faithfulness to you.’
“But St. John goes even further when he affirms that "’God is love’: God's very being is love. By sending his only Son and the Spirit of Love in the fullness of time, God has revealed his innermost secret: God himself is an eternal exchange of love, Father, Son and Holy Spirit, and he has destined us to share in that exchange.”
Catechism 218-221