Answer:
The reason is that the Americans didn't know that war was officially over and that the peace treaty was already signed. The peace was signed in December of 1814, while the battle happened in January of 1815.
Explanation:
We need to have in mind that in this information people still needed a lot of time to obtain certain information from different continent. Literally, you needed someone to transmit information by boat, and it usually needed a couple of months for it. It is interesting that Americans believed that this battle was decisive one.
USA and the UK are two different conglomerate of states in the world. USA, completely known as United States of America has a federal and constitutional republic form of government while the UK (United Kingdom) instills the constitutional monarchy-parliament governance. In this regard, the head of the state along with the representatives are elected into office by the people in the US. They do their roles as government officials under the code of an already set constitution. Conversely, the UK has its monarch who acts as the head of state and absolute power is not vested unto this monarch because there is usually a duly elected separate head of the government that exercises political powers. These leaders, like in the US, uphold a set of laws in the form of a constitution.
The legal realism approach treats laws as a tool that needs to be regularly reexamined and adjusted. It defines legal rights and legal duties as whatever the courts say they are whereas "natural law" treats laws as evolved to reflect the principles found in nature. It’s a body of unchanging moral principles regarded as a basis for all human conduct.