Yet now we suffer under two-party rule.
However, throughout our history, our two-party system has generally (with some notable exceptions) been able to work and work together. That's no longer the case. As such, it's hard to tell if the political polarization is a reflection of society, or if society is just adopting the polarization of our political elites.
So I stand by my original statement.
See, historically, when we spoke about parties, we really spoke about their respective establishments. The voters decided which one would be running the show at any given moment, but internal party politics were not readily accessible to the outsiders, and thus candidates and platforms were also vetted by the party establishment. Since establishment tends to be conservative by its very nature, this provided a screen against more extreme positions. To be clear: the politicians would still run on extreme positions, if they saw it as advantageous - but that didn't mean they'd govern accordingly if they won.
Then we got primaries. It's not that they didn't exist before - the first ones date back to before the Civil War. But they weren't anywhere near as common until the second half of the 20th century, and even then most were non-binding (and their results were often ignored when the "wrong" candidate won them).
And the primaries themselves changed over time, generally so as to broaden eligibility. In most other countries (where primaries are internal party matters), you have to actually be a member of the party in good standing in order to participate in that party's primary. The American system, where you merely need to register party affiliation in advance, is much more lax - and by now, even that formality is no longer necessary in many states.
So, voters now have a lot more influence over party politics. And this caused a nasty feedback loop, where agitprop that's thrown by the establishment at the voters, solely for the purpose of convincing them to vote one way or the other (appealing to emotions, especially fear and anger, since it's the most effective way), is regurgitated and injected into internal party matters and policies. So the party platform moves further away from the center, and its agitprop shifts accordingly, creating even more radicalized supporters, who again feed it back into the party etc.
Tea Party was a wake-up call in that sense, when a bunch of traditional Republican candidates lost to grassroots crazies who said mostly the same things, but who also sincerely believed in those things. Trump is also part of the same phenomenon - he might not be a sincere believer, but he appears as one to his followers. And there's some evidence of similar processes happening in the Democratic party. Slower, because its electorate is a broader coalition with more conflicting goals, and so the direction in which the voters move the party is less clearly defined. But you can see the internal radicalization spill out on some issues already, and there's more to come.
If you have people in 5 parties to vote for in your riding(district?), then first past the post is the only way it works easily! Seldom will one of those 5, get 50.1% of the vote!
And why would they? The most popular wins, the people have spoken.
The main reason FPTP ensures at most 2 parties is that, say you have parties 1, A, and B, where A and B are relatively similar to each other. And say A and B are together more populous than 1, like a 40/30/30 split.
By splitting those 60% mostly-similar votes between A and B, both lose to the less-popular 1. It becomes in A and B's best interest to not cannibalize each other's votes, i.e. merge and dominate (or at least compete). The less fragmented ideology wins, not the most desired.
It's even more compelling during the formation of new parties when there are only 2: by not voting for one of the two dominant ones, you are literally throwing your vote away because it has no chance, and it's worse for your ideology than if you had chosen the most-similar of the dominant party.
Worse yet, because most FPTP elections only require plurality for victory, you can have a party get less than 50% of the vote in each district (but more than any other party), and still take all the seats. In which case you literally have the minority running the country - so much for "people have spoken".
The key word there is easily. Now that we have computers and instant communication we can do things that would be/used to be considered hard but give better outcomes.
I'll also point out you don't need a winning party in an election you just need to be able to form a government and there's no reason 2 closely aligned parties can't work together or even traditionally opposing parties.
Additionally, why do we need to have a single representative for any individual instead of say 10 people representing a larger district?
One party would only have internal competition.