The Sadducees party was composed primarily of wealthy, sophisticated Jews who made the business of the temple their primary interest in life. Though small in number, they were very influential. Because they accepted only the Pentateuch as authoritative, they rejected the rabbinic oral tradition, which was more open to the possibility of resurrection from the dead.
Paul goes on to explain to them how the resurrection is foreshadowed even in the Pentateuch. God revealed himself to Moses as the God of his ancestors (Exodus 3:6,15-16), not just the God of those who were alive at the time. So if he is the God of the living, then Abraham and all those who came before must be alive in some way. One can deduce from this that there must be an afterlife.
The Sadducees had created an intellectual and spiritual elitism that blinded them to the full spectrum of how God works. St. Paul wanted to show them that God is too big and his word is too expansive for anyone to believe that he or she can understand it all. Our Lord’s life and ministry showed that God often moves in ways that seem new or unexpected to us. The resurrection is our greatest hope and joy, and yet the Sadducees, with their limited view of God and his word, risked missing this wonderful promise. May we never be like the Sadducees and narrow our horizons.