But you are still one person, Jesus and the Father are two separate beings, just like you and your father are two separate beings, how can you be one with your father?
Strictly speaking, God the Father and God the Son are not separate beings. They are distinct persons within one being.
One of the earliest responses on this thread had it very right – God is one, but God is not solitary. God is a relationship, even without considering any of the non-God creatures with which He also has relationships. Otherwise God, in and of Himself and without Creation, could not be Love, and we know that He is.
As a being, a “what,” God is singular. He has one nature, one mind, and one will. He does not have parts or divisions, He does not change within Himself, and He experiences no internal conflict.
As Persons, the “who” of God, God is three. Not only can we relate to God in three different ways (as Father/Creator, as Son/Redeemer/Brother, and as Spirit/Guide/Sanctifier), but those distinctions and relationships actually exist within God – not as parts or conflicting beings, but solely as love relationships within the one being of God. (That’s the main difference between orthodox Trinitarianism and Modalism – the Trinity isn’t just a fact about our relationship with God, but a fact about God Himself apart from any creature.)
But Jesus was fully man and fully God, this seems to be two natures.
Yes, since the Incarnation, Jesus has two natures. But even though they come into contact when we consider the question “Who and what is Jesus,” we must not confuse the Trinity and the Incarnation.
God, as God, has one nature (one “what”) but is three persons (three “whos”). That’s the Trinity.
At a specific point in time, one of the three Persons (the one revealed to us as the Son) took on a human nature in addition to the divine nature He shares with the other Persons. He’s now one “who” but two “whats” (divine and human). That’s the Incarnation. Jesus’ human nature does not infiltrate or change His divine nature, which remains the same eternally, but is now inextricably united to it in such a way that everything experienced by Jesus as a human (birth, death, anxiety, obedience) can truly be said to have been experienced by God, and the attributes that apply to God (universal kingship, power over life and death, etc.) can truly be applied to the human.
When we see Jesus speak of God as greater than Himself, or distinguish His will from God’s, that’s not referring to a conflict between the Son and the Father (who are co-equal and always in agreement) but between Jesus’ human nature and will and His divine nature and will.
God is three Persons who are distinct enough to have true relationships with each other, but share one nature, mind, and will. Jesus is one Person (the same one that is the Second Person of the Trinity) with two natures, two minds, and two wills.
That’s how I understand the orthodox belief now, but it wasn’t always clear in my upbringing (first Protestant and later Catholic). For a very long time, I thought Jesus’ title of Son stemmed from the Incarnation (that he had been, in a non-sexual sense, fathered by God in the womb of Mary), and I think that’s what a lot of other people mean when they call him the Son of God, too. That’s also where you get the comparisons of Him with various demigods of mythology, like Dionysus or Heracles, who had a male god and a human woman as parents. But according to the Trinity doctrine, the Son is Son from all eternity, because His relationship with the Father is analogous to begetting/being begotten among humans. (Or, more likely, our father/son relationship is an imperfect analogy of theirs, but the relationship was revealed to us using human relationship terms.)
Usagi