The answer to this question is found in the very first paragraph of Chapter 16. In this chapter, the doctor is the narrator.
He says that there were only six of the mutineers left on board and he and the captain and the squire could have overcome them and taken the ship back. The only reason why they did not do this is because there was no wind.
The Hispaniola, of course, is a sailing ship. If there's no wind, it won't go anywhere. If they take the ship over and can't go anywhere, the other mutineers will just come right back to the ship and they (the captain and his followers) will be in trouble.
The men that were left on the Hispaniola contemplated committing mutiny and taking over the ship, but there was no wind and they would not have been able to sail. They knew they might have been caught by the other men when they returned. In addition, they found out that Jim Hawkins was not on board and they were worried about his safety. They could hear screams and it made the doctor fearful for Jim. The doctor and the captain did mutiny against the pirates so they could board the smaller ship and go to the island to find Jim.
Had there been a breath of wind we should have fall' on the six mutineers who were left aboard with us, slipped our cable, and away to sea.