I'm no historian - I can only go by what wiki and the history books tell me. And based on historical content, my interpretation is that Britain established unfair trade regulations - the US responded to prevent them from continuing them - and in essence, the Canadians, who strongly supported Britain with money, troops, etc. were caught in the middle. Unfortunately, when you pick a side in any war, you end up having to fight alongside them. The Canadians chose the side of the British in the War of 1812, and that's what essentially brought about the fighting between the US and Canada well over 200 years ago. I suppose it's possible that if the Canadians had chosen to remain neutral or at least determined not to support the British, it's conceivable that the US would have never attacked.
Not that I'm standing up to whether or not I personally believe they should have attacked either Britain or Canada in the first place - it was a different time back then, and who knows what factors played into that decision. It does seem like there was some interest in pushing British influence off the continent, which was probably a part of it. As RJ mentions above, the US may have provided some support to Napolean, who opposed Britain at the time, although I don't see that in any of the articles I've read (but it seems likely that it happened).
At least that's the way I'm reading it - and like I said, I'm no historian - I could be reading it wrong.