Why did the Sadducees object to Peter's preaching that Christ is alive?

The Sadducees objected because they denied any resurrection from the dead. Since they taught that people live and die like animals with no afterlife, Peter's preaching that Christ was alive and would return as King directly contradicted their doctrine, so they confronted him for teaching what flew in the face of their belief.

Les explains that the Sadducees were the group most concerned about Peter's preaching that Christ is alive and is yet able to come and be their King. They did not believe in resurrection from the dead; their doctrine was that you lived like an animal and died like an animal. Therefore, when the apostles taught through Jesus the resurrection from the dead, the Sadducees were grieved and came at Peter, saying, "How dare you teach something that flies in the face of our doctrine? There's no such thing as someone coming back from the dead."

Why were the Sadducees most concerned about Peter's preaching in Acts 4?

The Sadducees denied any resurrection from the dead, holding that people lived and died like animals. Peter's preaching that Christ was alive and could yet return as King directly contradicted their doctrine, so they were grieved and challenged him for teaching something that flew in the face of their belief.