A false dichotomy is the presentation of two options when more than two options really exist. Outside of formal logic and math, dichotomies do not exist. All choices which are strictly one-or-the-other are false. It is human nature to reduce choices to one-or-the-other. Such reductions are useful, but not accurate.

Example

Here is an example of a false dichotomy that's commonly applied.

There is a notion that people are either left-brained (logical, detail-oriented) or right-brained (creative, driven by intuition). This is broadly true, and left-brain / right-brain categorization can be a useful tool to sort people in instances like, say, while choosing high-school electives: creative people should take an art class, and logical people should take a computer class, because creative people like to do creative tasks and logical people like to do logical tasks.

Everyone has a natural tendency towards being left- or right- brained. That fact doesn't preclude people from transcending the category. People do all the time. Escape velocity is easy to achieve, with time and effort. Your pre-disposition is not a curse of pre-destination.

Broadly, polymaths display this transencendence, and arguably it's what makes them great at a wide variety of things. Albrecht Dürer was a great painter who created a number of drawing aids, called perspective machines, to help artists draw and understand perspective when the concept of perspective was still very new. Richard Feynman was a well-accomplished physicist, having developed quantum electrodynamics and the self-named Feynman diagrams, who enjoyed playing the bongos and who learned to draw around 1962, at the age of 44, for the reason he states below:

I wanted very much to learn to draw, for a reason that I kept to myself: I wanted to convey an emotion I have about the beauty of the world. It's difficult to describe because it's an emotion. It's analogous to the feeling one has in religion that has to do with a god that controls everything in the universe.

Finally, there are the traditional examples of gifted men with wide expertise like Ben Franklin, Thomas Jefferson, and those guys they named the four Teenage Mutant Ninja Turtles after: Leonardo da Vinci, Donatello, Raphael and Michelangelo.

The people enumerated here are all notable examples who defy reduction to a left- / right- dichotomy, but all cases need not be famous, polymaths, or anyone special.

Us Versus Them

One of the two reasons I understand dichotomies are constructed is to other some group. To create an "us" and "them". This tactic is polarizing and maybe a symptom of those wanting to incite Sensationalism.

Anything that benefits from increased readership or viewership can benefit from sensationalism because emotion, even anger, can drive the headlines that do iron man numbers. Headlines distilled from broad dichotomies and other generalities abound. Today this tactic is practiced largely by online content creators because their income is directly tied to audience click-through rate, viewership numbers, and how many people follow that affiliate link in the description. Newspapers whose bottom line is driven by subscriptions are less susceptible to this, thankfully, because a one-off paywalled article with a really upsetting headline does not meaningfully increase conversion. Online papers supported by advertising and affiliate linking, however, bend the knee.

Just an observation. I try to avoid sensationalism by staying off the parts of the Internet where it abounds, and by recognizing it when I see it and simply not engaging. Blocking web elements with uBlock Origin has been very helpful in scrubbing away comment sections and suggestions from YouTube when I just want to watch a video about something I am interested in in peace.

Mind the Gap

The other reason I've hinted at of why these dichotomies are constructed is: it makes the world easier to reason about. And generally they're correct. Most people fall neatly into a left- / right-brain dichotomy. Most people are either male or female. Most people are strictly introverted or extroverted. Most people are either leaders or followers. Most people see themselves as either one or the other.

Few have the knowledge that the chains that bind them are artificial, that the boundaries are arbitrary. Fewer care to cross the gap.