The first reason why the United States fought Britain in the War of 1812 was to end the practice of impressment against American sailors. The United States traded with Britain and France during the War of 1812, going against blockades in both countries. Britain impressed American sailors onto its ships in order to maintain its own merchant marine. The United States claimed that it was free to trade with whomever it wished, and that British impressment was an insult to American sovereignty.

The second reason was the belief that Britain incited Native American attacks against American settlements in the Great Lakes region. British forts still occupied the area despite the ruling of the 1783 Treaty of Paris and many tribes traded at these forts. The main source of settler/indigenous animosity was white encroachment on Native lands.

Finally, there was a small group in Congress called the "War Hawks" who thought that the United States should annex Canada. It was their belief that the Canadians (who were British colonial subjects at the time) would welcome the Americans as liberators. They thought the period during the Napoleonic War would be perfect for this annexation, as Britain was not paying attention to its Canadian provinces. The Canadians fought off the Americans in their poorly managed invasion, and the British army turned out in force to repel the invading Americans.

The United States went to war against Great Britain in 1812 for the following reasons:

• the belief (not entirely incorrect) that the British government was supporting, even encouraging, Native attacks along the Northwest frontier. The attempted pan-Indian revolt led by Tecumseh and his brother Tenskwatawa that was finally destroyed as part of the War of 1812 was seen as the product of British machinations. 
• the impressment of American sailors by the British navy. This practice had been ongoing for some time. Suspecting American ships of harboring deserters from the Royal Navy, British captains would often take American ships by force and force sailors--those suspected of desertion--to serve on British ships. This was part of a larger issue of free trade and freedom of the seas that emerged from the Wars of the French Revolution and the Napoleonic Wars in France.
• a desire by many Americans to wrest parts of Canada from the British Empire. This was a popular motive among many of the "war hawks," a group of young politicians who clamored for war. These men saw the elimination of  British influence in Canada as the only means to end British meddling on the frontier, and believed it would open the way for further territorial expansion by the young United States, already doubled in size since the Revolution by the Louisiana Purchase. They also saw the first two issues listed above as intolerable affronts to the nation's honor.