There are some ambiguities to the question; do you mean "why didn't Canada join the U.S., and instead stay with Britain?" That's been answered in some depth before, and is in the F.A.Q., I believe.

If you mean, "how did U.S. and British relations in the 1860s lead to Canada's Confederation?", well, that's a bit trickier. Britain had a few wars going on at the time, and didn't like the expenses of the colonies north of the U.S. They were already pulling troops out of Canada, PEI, New Brunswick, and Nova Scotia when the U.S. Civil War broke out in earnest, leaving those colonies relatively vulnerable, something that had people rather rightly concerned; forming their own country would allow the sharing of expense for a standing army.

As well, a railroad was wanted to connect the colonies and increase trade, hopefully improving everyone's fortunes. They didn't want to send the railroad through the U.S., though that would have meant a more direct route, because of the war, and the risk of Fenian raids (Fenian raids had the effect of actually pushing the railroad north through New Brunswick, rather than straight across). As well, the cost of the railroad wasn't helped by Britain, but was left to the colonies themselves, leaving them rather in debt. Canada, as part of its wooing of the Maritimes, offered to take on a lot of that debt.

There was also some animosity by then between Britain and the U.S. This, coupled with the bad feelings of U.S. occupation of Montreal during the war of Independence (and the fighting during the war of 1812), the "Manifest Destiny", and the occasional spilling north of the border of the Civil War, as well as piracy and privateering, meant a general distaste for joining the colonies, at least by some (if not most), and most of those some were in power at the time. There were towns that would have liked to have joined the U.S., Yarmouth being a good example of this. But the political engineering meant they didn't.

There's a lot to be said for Francophone/Anglophone relations, as well; while Anglophone Canada has never been particularly good at working with Francophone Canada, on something so big it would be difficult to work against, as well, and Francophone Canada, for the aforementioned invasion and the already high concerns about losing their culture, had no desire whatsoever to let the U.S. come near them.

So, with greater need of defense, a war spilling north, money being tight, and a great deal of pressure from the British Colonial Office to do something other than be an economic weight around the British neck, the colonies decided to become their own country, with plenty of goodwill toward Britain built into the formation.