It wasn't for lack of trying.

One of the first acts of the Continental Congress in 1775 was to dispatch Benedict Arnold north to try to conquer Canada. He managed to take Montreal, but failed to take Quebec City after the British threw them back after a short and disastrous siege. French-speaking Canadians were mostly lukewarm on the war at the time. They didn't like the British, but they didn't much like the Americans either, as they had centuries of bad blood and frontier warfare only recently concluded in 1760. American Revolutionaries didn't want to provoke them to join up with the British by attacking them but didn't trust them enough to serious consider having them join the new country, so they mostly left them alone.

The conclusion of the American Revolution saw a major influx of American settlers surging north into what is now Ontario, New Brunswick, and Nova Scotia. These were mostly Loyalists and former slaves who had been promised their freedom by the British, all of whom had a grudge against the Americans and a desire to stand apart from them. They were joined by more American settlers in the 1780s, but these migrants came more for the promise of land granted by the British than any loyalty to the crown.

Tens of thousands of former Americans had come to live in Canada by the outbreak of the War of 1812. The USA struck north first into Canada, seeking to attack and conquer the closest manifestation of British power on the continent. Most were lukewarm on the war itself and just wanted to be left alone. Some were deeply attached to their American homeland and welcomed the America army. Some, especially the Loyalists, adamantly opposed the Americans and fought to check their advance. First Nations, especially the Mohawks, were the primary hindrance to American advance at these early stages rather than the Canadians or the British.

Americans might have been able to take Canada if they had behaved themselves. American militiamen and army regulars pillaged the countryside in frustration after numerous defeats at the hands of the Mohawk war bands and British regulars. This turned the locals against them and prompted many settlers to join the local militias just to spite them. The war turned what had previously been a very fluid region of uncertain loyalty and identity into a more clearly-defined space. There was little sense of a Canadian identity in the region before 1812, but it began to take shape during the war as a direct result of American attempts to take the region.

Source:

Alan Taylor, The Civil War of 1812