Article Five of the United States Constitution
At the time, Congress thought that this would be the more democratic option.  A large majority of the people in the United States wanted the 21st Amendment to pass.  However, Congress thought the state legislators would refuse to pass the amendment because of pressure from powerful groups that were against alcohol.  In other words, Congress did not think that the state legislatures would vote the way the people of the United States would want.  This example shows why the Founding Fathers included the "ratifying convention" option in the amendment process.  If the state legislatures get too powerful, or do not represent what the people who elected them want, the people have the power to pass amendments too.