Tecumseh was a minor player in the causes of the War of 1812. The war began because American merchant seamen at sea were having their ships stopped by the British Navy on the high seas. British officers would come aboard, and seize random American seamen and impress them, which means to basically kidnap them and put them to work in the British Navy on British ships. This didn't just happen once, but dozens of times. You can't go around permanently stealing another country's citizens, and expect nothing to ever happen. There were also tensions between the U.S.and Britain regarding the status of Canada, and the Canadian border, and yes, Tecumseh too, but he was really just emblematic of a much larger Canadian problem. . There was a faction in American politics that thought most or even all of Canada should become part of America too. Lastly, (and most of the history books completely overlook this one) the British were also somewhat spoiling for a fight with the Americans. The British military at the time was cocky and at their fighting best, fresh from handling 20 years of war with Napoleon in Europe, so there was also a tad of payback in mind, as the British memory of having lost the American Revolution was still a recent painful memory. The British didn't believe America was strong enough or organized enough to fight them or protest their actions in any kind of organized manner, and for the most part, they were right. America finally did get roused enough however, and after a series of protests, President James Madison finally asked for a declaration of war from Congress, and got it.
Militarily, the war mostly did not go well for America, and there was a series of military disasters at the start of it culminating in a botched American invasion of Canada. This invasion included the burning of the Canadian equivalent of the White House in Toronto. The British returned the favor by invading Maryland and Virgina in the following year and burned the U.S. White House. The Maryland invasion included an attack on Fort McHenry in the harbor of Baltimore, and Francis Scott Key, who was an American who had been temporarily imprisoned on a British warship in the harbor, watched the all-night long bombardment of the fort by the British Navy. The next morning, when most observers had expected the fort to surrender, there was instead a large American flag still flying. This moved Key to pen the lyrics for the Star Spangled Banner, which was later published in newspapers around the country after his relase, and later was set to music as our national anthem. There was some U.S. military success at sea however, with the construction of 6 super strong frigates, the most famous being the USS Constitution, and a noted naval battle on Lake Erie which the U.S. also won. Overall though, the US Navy was far, far outnumbered by the much stronger British Navy. The final land battle of the war was the Battle of New Orleans. In this battle, future President Andrew Jackson pulled together a ragtag force of American soldiers, militiamen, civilian volunteers and even paroled pirates, to take up a defensive position against the attacking finest Highlander regiments in the British Army. Due to some very well organized and concentrated defensive musket and cannon fire, the battle was a huge lopsided American victory with 7 British soldiers killed for every American soldier killed, and then right after this, news of the peace treaty arrived. Due to the delay in news traveling across the Atlantic, the Battle of New Orleans was actually fought after the peace treaty had been signed and the countries were technically at peace. The American newspapers made much of the fact regarding the final American win in New Orleans however, and so this win remained strong in the American mindset. American history books of the last century tended to also spin the result as a notable American victory overall, when in reality the war was militarily a draw and basically a heavy mutual mauling on both sides. Politically however, impressing merchant seamen stopped, and the question of Canada remaining its own sovereign nation was also forever settled.
