“Regarding his Son, who as to his human nature was a descendant of David, and who through the Spirit of holiness was declared with power to be the Son of God by his resurrection from the dead: Jesus Christ our Lord” (Romans 1:3-4)
It is important to see Jesus in light of his humanity and divinity. Both natures had specific roles to play in the redemption of mankind. This is why Paul opens this letter with the revelation of this duality.
In this letter, we learn the gospel promised beforehand that God’s Son Jesus was a descendant of David. For the Jews, this would have been critically important information. Beginning in Genesis and going forward, there were many prophecies about the lineage of the Christ coming through the line of King David. I doubt few people would have listened to Paul’s claims if Jesus hadn’t been a descendant of David.
However, what I find fascinating is that Christ had any ancestors at all! Simply put, Jesus had ancestors because He had a human nature. And guess what? A human redeemer was also a promise foretold in the scriptures.
"The gospel he promised before hand through his prophets
in the Holy Scriptures..." (Romans 1:2)
If you look at the account of Paul's life in the Book of Acts, you'll see he was constantly defending the gospel before masses of people, Jewish leaders, the Roman government, and even before the original Apostles who learned directly from Jesus. I think this was because the gospel was so radically different than anything that had previously been taught and so the natural tendency was to question it.
Here's a beautiful truth: the very same gospel that Paul preached was promised throughout the entirety of the scriptures. Even today, we have a hard time understanding this, as I imagine the Apostle Paul did at first. In his own words, he admits to being faultless concerning legalistic righteousness (Phil. 3:6)—meaning he followed the letter of the law, which he knew inside and out and lived every moment making sure he was doing all that the law required. Some things don't change, for example, how many of us are like this today?
Imagine how mind-blowing it must have been to encounter Jesus and then to start piecing together everything the law and prophets talked about, which included everything Paul previously misunderstood while trying to do all that the law required. Imaging waking up to the fullness of what those things actually revealed—Jesus! This incredible revelation was so profound that Paul immediately set off for the desert of Arabia and spent three years sorting it out (Gal. 1:11-12, 17-18).