How Can Jesus Be Fully God and Fully Man At the Same Time?

Answer 1:

A contradiction can be defined in the terms "A=not-A"; a non-contradiction, in the terms "A≠not-A".
• The statements "Jesus is fully God" and "Jesus is fully man" don't involve such a contradiction, i.e, they don't say "Jesus is fully God," and "Jesus is not fully God" at the same time.
• Christian theology doesn't claim to say that Jesus is not God when it says Jesus is Man; likewise, it doesn't clam to say that Jesus is not man when it says that Jesus is God.

Answer 2:

• The divinity of Christ is eternal and immutable; therefore, in the Incarnation He was fully God. He was not created; He pre-existed. He was not born out of a man-woman relationship; but, was born of a Virgin; because He incarnated, He didn't come into being - there was not when He didn't exist.
• In the Incarnation, God partook of human nature; He could do that because He created the world and so the world belonged to Him and He sustained it. The world didn't cut off from Him in a way that God and creation were unrelated to each other. The world had not become a "wholly other" to God. The world was not closed out to God, as if it were an infinite and absolute entity by itself. The fact was that the world was contingent on Him. The world couldn't restrict His power. In fact, it was He who held it by the word of His power (Heb 1:3). The world is not eternal; it is temporal; therefore, it is impossible for the world (including man) to become God. That would be a contradiction of terms. However, the Second Person of the Divine Trinity did become man, because His creation was not beyond His reach. The temporal exists within the eternal; and the finite within the infinite (not vice versa). "In Him we live and move and have our being." (Acts 17:28). This is not pantheism or panentheism. It doesn't say the world contains God as its soul or the world is God; but, that the world is contingent upon God, therefore not beyond His reach. Miracles are possible, Divine intervention is possible (the universe is not closed) and the Incarnation is the greatest example of God's intervention in human history.

Further Reading:
The Humanity and Divinity of Christ
The Logic of Faith