This is because they believed the federal government would then have more control over what the states did. The states are supposed to be free to make their own laws without federal involvement.
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Alexander Hamilton proposed that the federal government should assume the debts that were owed by states. This was opposed by many Americans because it would mean states that had already paid their debts would have to cover for states that were still in debt.
Alexander Hamilton believed the Federal Government was more intelligent about money than the people. The whole concept of a national government assuming all debts owed by the states puts the government in a power position with no freedoms for the state rights or people.
It is in essence a National Dictatorship with the bureaucrats holding states up to corruption at the highest level.
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The South supported it because it could have allowed new slave-states. The Northern abolitionists opposed it for the same reason.
The southern states because the Second Great Awakening promoted the abolitionist movement.
Several states feared the strong federal government and wanted the BILL OF RIGHTS added.
Abraham Lincoln did not believe that he needed to compromise with the South on the issue of expansion of slavery in the Territories. He thought that the Southern States were bluffing and would not leave the Union.