Hamilton knew about how the Bank of England created their money and he wanted the United States to have its own bank with many branches around the States that could create a single currency.
Thomas Jefferson opposed to the idea. In his opinion, States should be able to charter banks that could issue money.
In addition, he also thought that the constitution did not grant the federal government any power to create a national bank.
Hamilton, on the other hand, believed that the constitution gave the national government plenty of power for such a bank to be established.