I'm not ragging on the US or anything; please read the whole writeup before judging on the title.
Why should someone train to get a private (non-commercial) pilot's license outside of the USA?

The really short answer:
Your license will not be internationally recognized if obtained from the USA.
The short answer:
A pilot license obtained in Canada is valid worldwide, in every country that has a public airport. Australian and British licenses are valid in most countries (including the United States), and a license from the United States is only valid within the United States*.
The long answer:
US flight training is equivalent, if not better, than any other country's flight training regimen (depending on the actual school, of course). The first, most important thing to note is that US technology is cheaper, more widespread, and moreso government-funded than any other country. This means that a lot of equipment (such as airport lighting and radar coverage) is more up-to-date and easier to use than equivalent facilities in other countries. What this usually means is that US pilots are not versed, or have forgotten, what to do at airports without all the high-tech add-ons... Essentially, US pilots are spoiled. The biggest negative thing about a US license, however, is the fact that there is not a square foot of US soil that does not have radar coverage. What this means is that, as long as you aren't flying in a valley or otherwise below radar, someone is always looking at you. You can always get on the radio and ask for help. There is always a fallback - and therefore, emergency procedures and navigation by map becomes a forgotten relic.

Example of a US flight:

Pilot: "I'm ready for takeoff!"
Tower: "Ok, you are cleared for takeoff."
Pilot: "Thanks. By the way, how do I get to Seattle?"
Tower: "No problem; turn to a heading of 156 degrees and contact this certain radio frequency once you pass over that big lake there."

Example of a Canadian flight (small town, no tower):

Pilot: "I'm taking off now!"
Pilot: "I'm in the air now!.. Uh... I'm going to seattle!"
Pilot: "I guess I'll have to look at my map and figure this out for myself..."

Example of a Canadian flight (with tower):

Pilot: "I'm ready for takeoff!"
Tower: "Ok, you are cleared for takeoff."
Pilot: "OK thanks. By the way, how do I get to Seattle?"
Tower: "No problem; just refer to map A4."
- or
Tower: "We're too busy to deal with your request."
Pilot: "I guess I'll have to look at my map and figure this out for myself..."

Example of a US pilot that is lost:

Pilot: "Help! I'm lost!"
Radar: "I see you; you're going to Seattle right? Turn to heading 187 degrees and you'll get there in about 30 mins at your current speed."
Pilot: "Thanks buddy!"
Radar: "That's what we're here for."

Example of a Canadian pilot that is lost:

Pilot: "Help! I'm lost!"
Pilot: "Help!"
Pilot: "Is anyone out there?"
Pilot: "I'm landing on this old logging road! If anyone can hear me, please call in!"
Pilot: "I'm eating my co-pilot to survive!"

As you can see, it is very easy for a US pilot to get "lazy" and forget half of the standard protocol, just because it is redundant or uneccesary at most locations in the USA.

I'm not by any means saying that ALL pilots from the USA are horrible; I'm just saying that every other country in the world figures there is a large enough lazy US pilot population to be considered a risk to their airspace.
*: When I say the US license is only good in the US, it is important to note that it is also valid in Canada and in Mexico but only if you fly in a radar-monitored area. There is very little radar coverage in Mexico and only the area immediately north of the Canada-US border has radar coverage. So yes, you can fly to any major Canadian city with a US license. All US-licensed-flights in Canada must also have filed a complete flight plan, even if it's a 5 minute sight-seeing tour... Though required by law this isn't usually enforced, however.