Well, the simple fact is, we’re not. We believe in one God. There are three relationally distinct Persons in One Being. But not three gods. They all perfectly possess the one and the same divine nature.
I think he’s under the (understandable) impression that the person/being ratio must be 1:1. But point out to him this isn’t the case, even in our own experience. A statue is a being. It exists. But it’s not a person. If we can have a being that exists as zero persons, and a being that exists as one person, why can’t we have a Being that exists as Three persons?
We’ve never experienced that, but I think your friend would agree that the almighty God should transcend our experiences.
I also think this analogy by St. Augustine would be helpful to show him how it’s not irrational to say there can be three relationally distinct realities in only one being:
I speak of these three: to be, to know, and to will. For I am, and I know, and I will: I am a knowing and a willing being, and I know that I am and that I will, and I will to be and to know. Therefore, in these three, let him who can do so perceive how inseparable a life there is, one life and one mind and one essence, and finally how inseparable a distinction there is, and yet there is a distinction. Surely a man stands face to face with himself. Let him take heed of himself, and look there, and tell me. But when he has discovered any of these and is ready to speak, let him not think that he has found that immutable being which is above all these, which is immutably, and knows immutably, and wills immutably.
In God, the Father is the being one, the Son is the knowing one, and the Holy Spirit is the willing one. Just like in us, these three are really distinct, but they also subsist in one being.
Now obviously this isn’t perfect, no analogy is. Our knowing, being, and willing are not each infinite as the persons of God are. They subsist in one being in us, but they are not persons.
None of this will probably convince him, but I think if you give him these two examples, it might help him see why we’re not polytheists.