What is so amazing about the fact that Jesus had a human mind (Luke 2:52, Hebrews 5:8)? Everything. If He did not have a human mind then we would all get what we deserve and be in Hell.
I have been absolutely amazed at the depth of the gospel lately. The gospel is something that is so in depth, we will never understand it. The deeper we dig into the intricacies of the gospel the more layers we see of it. What does it mean when the Bible says that Jesus emptied himself (Philippians 2:5-7)? Did He give up attributes in the incarnation? Which attributes of Deity did Jesus possess on earth? Was He omniscient and omnipresent while on earth? Your answers to these questions are so crucial that if you are wrong then you are believing some of the heresies that have been held throughout the ages. If you are believing something about Jesus that is not true then you are believing in a Jesus that does not exist.
Here is a good place to start concerning the humanity of Christ. Jesus did not have to become like an angel, He had to become like a man because God was concerned with saving men, not with saving angels. Why did Jesus have to be fully man?
1. Jesus had to be fully man in order to be our representative and obey in our place. (Romans 5:18-19)
2. Jesus had to be fully man or He could not have died to pay the penalty for man's sins. He could not have been a substitute sacrifice for us. (Hebrews 2:16-17)
3. Jesus had to be fully man in order to fulfill the role of mediator. (1 Timothy 2:5)
4. Jesus had to be fully man in order to fulfill God's original purpose that man rule over his creation. (Hebrews 2:8-9, Ephesians 1:22, Revelation 3:2)
5. Jesus had to be fully man in order to live as our example and pattern of life. (1 John 2:6, 3:2-3, 2 Corinthians 3:18, Romans 8:29, 1 Peter 2:21)
6. Jesus had to be fully man so that He could be raised as a man in order to be the "first-born from the dead." (Colossians 1:18), the pattern for the bodies that we would later have.
7. Jesus had to be fully man to sympathize more fully with us in our experiences. (Hebrews 2:18)