Actually Christ did say He was the Son of man AND the Son of God, and is addressed as the Son of God throughout the scriptures;
Jesus answered: "Don't you know me, Philip, even after I have been among you such a long time? Anyone who has seen me has seen the Father. How can you say, 'Show us the Father'? John 14:9,10
"I and the Father are one." John 10:30
"This sickness will not end in death. No, it is for God's glory so that God's Son may be glorified through it." John 11:4
Why then do you accuse me of blasphemy because I said, 'I am God's Son'? Do not believe me unless I do what my Father does. John 10:36,37
"I tell you the truth, whoever hears my word and believes him who sent me has eternal life and will not be condemned; he has crossed over from death to life.
I tell you the truth, a time is coming and has now come when the dead will hear the voice of the Son of God and those who hear will live." John 5:24,25
Why then do you accuse me of blasphemy because I said, 'I am God's Son'? John 10:36
They all asked, "Are you then the Son of God?" He replied, "You are right in saying I am." Luke 22:70
"The virgin will be with child and will give birth to a son, and they will call him Immanuel which means, "God with us." Matthew 1:23