Because if God wasn’t a Trinity, then he wouldn’t be inherently loving:
If God exists but is unipersonal, then there was a time when God was not love. Before God created the world, when there was only one divine person, there was no lover, because love can exist only in a relationship.
If a unipersonal God had created the world and its inhabitants, such a God would not in his essence be love. Power and greatness possibly, but not love. But if from all eternity, without end and without beginning, ultimate reality is a community of persons knowing and loving one another, then ultimate reality is about love relationships.
Why would a triune God create a world? If he were a unipersonal God, you might say, “Well, he created the world so he can have beings who give him worshipful love, and that would give him joy.” But the triune God already had that—and he received love within himself in a far purer, more powerful form than we human beings can ever give him. So why would he create us? There’s only one answer.
He must have created us not to get joy but to give it. He must have created us to invite us into the dance, to say: If you glorify me, if you center your entire life on me, if you find me beautiful for who I am in myself, then you will step into the dance, which is what you are made for. You are made not just to believe in me or to be spiritual in some general way, not just to pray and get a bit of inspiration when things are tough. You are made to center everything in your life on me, to think of everything in terms of your relationship to me. To serve me unconditionally. That’s where you’ll find your joy.
From King’s Cross by Tim Keller