Actually, most European countries are divided as well but we typically have a proportional representation with a 4-5% minimum which means we have more than two choices which creates an entirely different dynamic. Now naturally it divides itself into blocks it means there can be 2-3 different directions and 2-3 specialist parties that support their side and their relative strength matters. I'm guessing with a European system you'd have Democrats, Liberals, Republicans, Christians, Tea Party, Libertarians and Greens. Suddenly you're not losing just a few swing voters, you can lose voters in any direction.
Forming a new party actually has meaning as a 30% party and two 25+5% parties have the same power, unlike the US system where starting a party competing for the same voters spells doom for everybody. I used to think our system was worse because of all the compromises and coalitions and in-fighting, but really all the US system does is bring all those warring factions together in the same party. All the bargain-making is just done between factions in Congress, not between parties.
And the voters don't get to be a part of that process, here there's different shades of red and blue that shift far more easily in the polls. If the voters think the conservatives aren't being very conservative or the liberals very liberal or don't think you're doing a very good job, there are other parties with similar politics that would be happy to take over. The politicians have to work all the time to convince the voters that their party is the right one, there are relatively few genuinely safe votes. Typically only 50-75% will vote for the same party twice in a row.
So I think it's the system, of course the only way to change the system would be getting an amendment through Congress so.... yeah, you're pretty much stuck with a two-party state that will flaunt a few divisive political issues while making sure their campaign contributors are happy. They're quasi-monopolists on each half of the political spectrum, they got no reason to want to change and the third parties don't have the power to change anything.