The best way to make an argument for classical economics is to argue that it fits with how human beings behave. You can argue that classical economics follows from the laws of supply and demand.
We know that the laws of supply and demand are true. When something costs more, people will tend to buy less of it. Therefore, to get people to buy more, you have to lower prices. When something sells for a higher price, suppliers will want to make more of that thing. These are common sense laws that everyone can agree on.
Classical economic theory flows naturally from these laws. For example, let us think about what happens if we enter a recession. If a recession occurs, people stop buying as many things. If people stop buying, suppliers will naturally lower their prices so that the people will be more likely to buy. If suppliers lower their prices, workers will realize that they do not need as much money to maintain their standard of living. They will also realize that their employers cannot afford to pay them as much. Therefore, they will accept lower wages. These are simply common sense moves that are predicted by the laws of supply and demand.
This is the best argument for classical economics. It makes complete logical sense because it relies on people being logical and acting in ways that common sense says they will.