Why is Jesus referred to as the son of David more than as the son of Abraham or of Noah?
Jesus was born into this world, which meant that he was a descendant of Noah, just as everyone else in the world since the flood has descended from Noah. "Now the sons of Noah who went out of the ark were Shem, Ham, and Japheth. And Ham was the father of Canaan. These three were the sons of Noah, and from these the whole earth was populated" (Genesis 9:18-19). Being a son of Noah did not make him unique, though Jesus often referred to himself as the son of Man. God took on the form of man and lived among us. "And the Word became flesh and dwelt among us, and we beheld His glory, the glory as of the only begotten of the Father, full of grace and truth" (John 1:14). "Inasmuch then as the children have partaken of flesh and blood, He Himself likewise shared in the same, that through death He might destroy him who had the power of death, that is, the devil, ... Therefore, in all things He had to be made like His brethren, that He might be a merciful and faithful High Priest in things pertaining to God, to make propitiation for the sins of the people" (Hebrews 2:14, 17).
Jesus was an Israelite, which automatically meant that he was a descendant of Abraham. To Abraham was the promise, "In your seed all the nations of the earth shall be blessed, because you have obeyed My voice" (Genesis 22:18). This seed, Paul tells us was Jesus. "Now to Abraham and his Seed were the promises made. He does not say, "And to seeds," as of many, but as of one, "And to your Seed," who is Christ" (Galatians 3:16). Yet, in a nation of Israelites, being a descendant of Abraham doesn't make a person stand out.
What made Jesus a rare Israelite was the fact that he was the heir to the throne of David. Kingship only passes to one person per generation and the kingship only belonged to those who descended from David. David received several promises from God that his descendants would rule forever. "But My mercy shall not depart from him, as I took it from Saul, whom I removed from before you. And your house and your kingdom shall be established forever before you. Your throne shall be established forever" (II Samuel 7:15-16). By referring to himself as the son of David, Jesus was taking on the narrowest definition needed to fulfill the prophecies of God. He was a man, an Israelite, and the rightful ruler to sit on the throne of David. "This Jesus God has raised up, of which we are all witnesses. Therefore being exalted to the right hand of God, and having received from the Father the promise of the Holy Spirit, He poured out this which you now see and hear. For David did not ascend into the heavens, but he says himself: 'The LORD said to my Lord, Sit at My right hand, Till I make Your enemies Your footstool.' Therefore let all the house of Israel know assuredly that God has made this Jesus, whom you crucified, both Lord and Christ." (Acts 2:32-36) . When we refer to Jesus as the Lord, it is to this prophecy and its fulfillment that we reference. Jesus is King!