I don't see the intro to Luke as being accurate. Matthew talked to Jews in his gospel. Luke talked to Greeks. Luke states the reason he wrote his gospel:

(Luke 1:1-4 NIV) Many have undertaken to draw up an account of the things that have been fulfilled among us, {2} just as they were handed down to us by those who from the first were eyewitnesses and servants of the word. {3} Therefore, since I myself have carefully investigated everything from the beginning, it seemed good also to me to write an orderly account for you, most excellent Theophilus, {4} so that you may know the certainty of the things you have been taught.