The answer to this question: Why would Jefferson oppose the National Bank?, is, A: Use of implied powers was unconstitutional.
The discussion between Alexander Hamilton and Thomas Jefferson, which took place in 1791, regarding the issue of if it was Constitutional, and correct, for Congress to create a National Bank, boiled down to each side using different articles in the Constitution itself, to argue their point. While Hamilton insisted that a National Bank would lend stability to the economy, and also equalize the currency used in the states, Thomas Jefferson argued that it should be the states the ones who took on that role. In the end, it all came down to whether the Constitution allows the government to make such a move, or not. In 1791, Congress passed the Bank Bill and established with it the Bank of the United States. Jefferson, in a last attempt at stopping it, went to President George Washington, who was the only one who could veto the Bill. Both Jefferson and Hamilton used the Xth Amendment and the “elastic clause” to argue their points of Constitutionality. Jefferson insisted that the Xth Amendment clarified that powers not specifically given by Constitution to the national government, must be defered in favor of the states and the people. Hamilton, with the “elastic clause” proved that Congress can enact any necessary laws that will ensure the stability and improvement of the Union. In the end, Hamilton´s side won the argument.