How can God have a son?
This is actually a question as old as the Bible itself. Jesus calling God his Father was scandalous to the Jewish authorities and was one of the reasons they would eventually arrest him. “For this reason the Jews tried all the more to kill him, because he… also called God his own father, making himself equal to God” (John 5:18). Such a thing would be blasphemous to any Jew, because it is a “mere man” calling himself God’s equal and God’s Son.
In the early Church, there were many debates over whether Jesus truly was divine–and if he was, did that mean he was equal to the Father? Was Jesus only like the Father? Was “Son of God” a title he earned or his very identity? Was Jesus the same Person as the Father, just wearing a different “mask?”
All these questions were the subject of many debates in the early centuries of the Catholic Church–debates so intense that they sometimes led to riots in the streets. It all comes back to those basic questions: “What is God?” “Who is God?” “Who is Jesus Christ?”
As far as the specific question of how God can have a Son, let’s start by framing the problem here.
We say that “God is one.” That means that there cannot be more than one God. We also say that “God is simple.” That is a special term that indicates that God is not “composite”–that is, he is not made up of different “parts.” God cannot be “split.” Yet at the same time, Jesus is God. The Creed says he is “God from God, light from light, true God from true God… consubstantial [of the same being] with the Father.” How is this possible? Well, this is what the doctrine of the Holy Trinity tries to articulate.
Let’s start by saying that God the Father does not “have a Son” the same way we as human beings “have a son (or a daughter).” The Father doesn’t “conceive” the Son. He also doesn’t “chop off” a part of his being to make the Son. Instead, we say the Son is “begotten” by the Father. So what does that mean?
Here is the key point: Whatever difference there is between the Father and the Son, the difference is not in what they are, but in who they are. In Trinitarian theology, this is sometimes referred to by the term “subsistent relations.” That’s a technical term, so let me explain it by making a comparison… We human beings have relationships with different people and things: I have a relationship with my father, I have a relationship with my coworkers, I have a relationship with my phone, etc. But in all of these cases, we say that I have a relationship. The Trinity is different. The Father, Son, and Holy Spirit don’t have relations; they are relations. The very essence of who they are is their relationship with one another.
So the divine nature that the Son and the Holy Spirit have is the same as the Father’s. But who they are is entirely different from one another. This can be a very tricky point to articulate. God’s not one person wearing three different “masks” or playing three different characters named “Father,” “Son,” and “Holy Spirit.” That’s a heresy known as Modalism. But God is also not three separate beings who just happen to be united in their will or their mission–that’s another heresy called Tritheism. God is one “thing” (the what), but God is three Persons who are really distinct from one another (the who). The mystery of the Trinity is very difficult to get right! That’s why it took the Church centuries to speak about properly!
Another thing to note is that we can say that God is “Father” in different ways. When we say he is the Father of the Son, we are referring to how the First Person of the Trinity is Father by nature. When we call him our Father, we are referring to how the First Person of the Trinity is Father by grace–specifically, the grace of our Baptism, in which we enter into Jesus’ own identity as the Son. When we call God the “Father” of the human race or of all creation, we are using “fatherhood” in a more general sense of the “origin of all being.” Here we actually apply this term to the Trinity as a whole, not just to God the Father. That is why Colossians 1:16 says that “through” Christ all things were made, and why Jesus calls the disciples “my children” at the Last Supper (John 13:33).
I hope this helps clarify your question! Speaking about the Trinity can be difficult because it requires precise language.