The mistake that Ben Stout makes is that he fails to identify the flag on the ship that is near them as being American. At this stage, America opposed slavery and set out actively to stop slave traders by sending out ships to apprehend and arrest those who were involved in it. This is why suddenly the Captain is forced to order his crew to throw his slaves overboard to face a watery death. For them to be captured by an American ship would have resulted in their imprisonment or worse. An English ship would not have bothered them, because at this time England itself was still profiting greatly from the slave trade. This explains the captain's loud response when he realises the ship is American and not English:
"By God!" Cawthorne thundered. "I see the ship. I see it. It's American! You disaster, Stout! You've murdered me! Get the slaves over! Get them over!"
Cawthorne's plans to make his fortune on this trip are ended when he realises that he must act quickly to save his very life and avoid arrest by getting rid of the incriminating evidence: the slaves themselves.