Plurality rule instead of majority rule. Basically, you don't win in american politics by having a majority of people, you just need to have more than anyone else. You can win an american election with only 35% of the vote, so long as the next guy only has 34% or lower. 2/3ds of the voters may not want you, but congrats you won anyway!
This means that no one can afford to vote on policy, because that risks dividing you base into more granular issues. If 20 people vote "A and B, but leaning towards A" and another 20 of people vote "A and B, but leaning towards B", both groups of people lose to the 22 people that voted "C and only C". The A-B group totals 40 if you add them together, and they really just want slight variations of the same thing, but that's not what the american electoral system is designed to support so C wins despite having was less people.
This means that in order to maximize your chance of winning, you have to have the broadest appeal possible, and the quickest route to glossing over internal disagreements about individual policy is to make the race entirely about beating the other side who is literally the devil so go out and vote.
tldr: in majority rule, you HAVE to compromise until you find a middle ground that enough people support that is forms a majority (50+%) which cuts out the extremes. In plurality rule, the only thing that matters is beating the other guy so you are increasingly encouraged to appeal to fringe groups and extremes in order to get that competitive edge. And that's why both American parties seem like they have lost their fucking minds lately: both sides just keep doubling down and doubling down on their own versions of extremist rhetoric.