I don't see this as a philosophical problem, but as the process of politics devolving into a sport. The point of a party is not to hold a coherent opinion. It is to win things,and in doing so either advance the causes of its partisans, or just make them feel better because they won. Splitting into more than two contending teams wastes leverage, when competing becomes the primary point of politics, which it often does.
Other countries (infamously Italy, and famously India, until recently) have more than two parties, and that allows those parties to have more individual viewpoints, at he cost of having all important legislative moves require a coalition process. In such an environment, it can be hard to keep a government together, especially if it tries to actually do things.
The meaning of right vs left has changed across time. Democrats were once the party in favor of guiding social conventions through large institutions, which included the Catholic Church and, in the South, the plantation system, which it wanted seen not as a system of oppression but a matter of individual morality. Republicans opposed them.
Clearly, Republicans now see themselves as the party in favor of established religion, including the Catholic Church, and want to see racism as not being bound to systematic oppression, but as a matter of individual morality. And Democrats oppose them.
The division is always into two camps, but those camps are not really defined in the same way over time. The right/left naming and orientation is common in a world of democracies shaped by European influence because it once expressed the relationship of the party to a specific European variety of feudal monarchy that contended with traditional limitations in a given way.
We create an artificial continuity back to the days of monarchy, when the monarchy and its selected Church represented the Right and all institutions limiting it, such as parliaments, business and labor as groups, principles of common law, and even other Churches, represented the Left. But we do so only for the sake of labeling, individual ideas have almost all been held by both sides over time.