Our government divides the country into a bunch of districts and forces each one of them to run a first-past-the-post election. Every position is first-past-the-post. The problem is that first-past-the-post seems to have a fixed point, where if parties get too popular they fragment over minor internal differences, or if not popular enough they polarize and demonize to try to suppress third-party turnout and collect those votes for themselves. The fixed point is therefore that 50% of the legislators belong to one party, 50% belong to the other, and everyone is filled with credulity for their own side and hatred for the other. And mathematical fixed-point theorems seem to be general enough to converge on this fixed-point.
It's worth pointing out that you can just look at the presidential election history and see a sequence of these convergences culminating in the US Civil War, and we seem to be falling back into it in the past several election cycles -- not just this last one.
What's even more interesting is that we use proportional methods in the States. The proportional system that you might know as the Sainte-Laguë system, we know as the Webster system and use to allocate House seats among the states. If we used something similar to elect parties to the House, we could probably keep the Senate and the Presidency the same and it would still give a sort of destabilizing effect to the two-party hatred-hegemony.