Final answer:
Andrew Jackson did not argue that 'free men of colour enjoy equal rights and privileges with white men' while recruiting black soldiers in New Orleans. Historical records show that free blacks faced discrimination and did not have equal rights as white men during that era. Therefore, the correct option is D.
Step-by-step explanation:
Andrew Jackson sought to recruit free blacks to defend New Orleans by appealing to the Governor of Louisiana using various arguments. The option that he did not use was D. free men of colour enjoy equal rights and privileges with white men. Historically, free blacks in America, especially in the South, faced significant discrimination and did not enjoy equal rights and privileges with white men. During the periods of the American Revolution and Civil War, the enlistment of black men, both free and slave, was a contentious issue, often avoided or restricted due to fears of armed slave revolts or the political implications of arming African Americans.
Despite some regions allowing for the recruitment of black soldiers, there was a clear distinction between the rights of white men and men of colour. Jackson himself promoted policies that limited the rights of free blacks and maintained the institution of slavery, which stands in contrast to the statement about equal rights and privileges.