Actually its a bit the opposite. Political science theory claims that the US, Canada, the UK, India and other First-Past-The-Post systems should have two parties. But all the others really aren't. So the question is why does the theory work for America and not for others.

Duverger's Law says that plurality voting systems with single member districts tend toward two-party systems, while the double ballot majority system and proportional representation systems tend toward a multi-party system. The reason for this is that if a voter has just one vote for just one office holder, there are lots of mechanics that drive out third parties.

First, a party that consistently finished second or third in a lot of districts will still win no seats. Therefore geographically thin but ideologically viable parties fail to break through.

Second, if there are 100,000 moderate voters and 80,000 radical voters, if two moderate candidates run against radical yellow candidate, the yellow candidate will win even though there are more moderates. So the moderate voters will seek information to decide who to coalesce their votes around to win.

What is unusual is that the U.S. actually is a strictly two-party system while the other plurality countries like Canada and the UK and India have multi-party systems, although typically with two or so dominant parties that compete for power.

Riker notes that strong regional parties can distort the system. For instance, in Canada, the Quebec-separatist Bloc Quebecois became the second largest party federally in the 1990s with just 14% of the vote by winning a number of districts with 35% of the vote against a divided set of federalist parties. Johnston argues that the Canadian system is multi-party because of the dominance of a centrist Liberal party due to a state of basically permanent regional instability.

So why did the U.S. follow the dominant law of empirical political science to have two parties when most other comparative polities have to explain why they do not? The Democrats or Republicans have finished first or second in national balloting since 1852, with the exception of Teddy Roosevelt's second place finish as a Progressive in 1912. Since the Second World War, no more than two of 535 members of Congress were not members of those two parties.

One reason is that the United States is one of the few jurisdictions that allows sub-national states or provinces to determine the rules for local balloting for national elections. That makes it very difficult to just get on the ballot nationally, and makes running for national office incredibly complex. Frankly, those sub-national rule sets are easy to rig to make third-party entry difficult.

It also allows for easing or restricting votes by economically or legally alienated groups to make local races safer. Elites can coalesce around a single dominant party and insurgency be captured in the second party by region.

Second, the rules for running for national office reward containing insurgency within two parties and deeply punish third-parties. The Presidential electoral college system in 48 states further enhances the winner-takes-all characteristic of voting, making the complexity of assembling a majority of electoral college votes a near impossibility for a third-party. Note that Ross Perot got 19% of the vote and not a single electoral college vote in 1992.

The primary system offers an institutional safety valve to contain ideological and anti-establishment insurgencies within the two-party system. Anger at Washington can be contained to overthrowing the sitting representative for an angrier version from the same party.

The third is because of the role of race in American politics. Blacks and southern whites act as fairly durable voting blocks, and political parties use these two blocks in opposition. The two parties typically pursue one block and are challenged with the other. When third party candidates ran for President and successfully gained electoral college voters (Wallace, 1968; Thurmond, 1948), they were a holding vehicle for southern whites who were transitioning out of the Democrats because of the party's pursuit of black voters.

These two blocks are the largest and reinforce the two party system. American parties are successful when they can maximize turnout in one group while minimizing the electoral impact of opposition from the second. Philpott goes one step further to argue that political parties are responsible for actively creating the wedge between these groups to mobilize voters and construct winning voting coalitions, and clearly signal their position on this cleavage to voters.

The result is that the rule-setting mechanism, institutions and voting cleavages of American politics reinforce a two-party system to a greater extent than other plurality systems.

Johnston http://policyoptions.irpp.org/magazines/october-2017/the-baffling-history-of-canadas-party-system/

Riker https://www.jstor.org/stable/1962968?seq=1#page_scan_tab_contents

Philpott https://www.press.umich.edu/pdf/9780472099672-ch2.pdf

I would like to challenge the claim that we have actually been a two party system. On the surface it's true but V. O. Key documents in his book "Southern Politics in State and Nation" that in fact that Democrats in the South during the first half of the 20th century often (though not always, see Virginia) had multiple competing sides within the state.

Further Nicol C. Rae's "Southern Democrats" documents a major split within the democratic party in the 80s which pit centerists against liberal or progressive Democrats.

The system doesn't enforce two parties but because the system tends to generate two parties much of the politics moves within the parties of the moment and there are separate parties within the parties. For at least most of the 20th century there have been multiple parties who don a common label.

You may want to familiarize yourself with Duvreger's Law; essentially - and various math models show similar "degenerations" - it holds that plurality-rule elections (such as first past the post) structured within single-member districts tend to, after several voting iterations, lead to two entrenched parties.

It's a result of vote-for-one, which convinces voters not to support their favorite 3rd party, because it's a wasted vote. The only way to have successful 3rd parties is with voting systems that let you safely vote your favorite, like Approval Voting or Score Voting.