False Dichotomy means taking a complex issue, and boiling it down to 2 simple mutually exclusive choices, when in reality there’s more alternatives available. To make their side look more appealing, people present nuanced arguments as black and white, or take extremes and pretend like they are the only options.
This kind of thinking often leads to ignoring potential solutions, and prevents us from gaining an accurate understanding of the situation.
It also leads to polarization of opinions — people treat an argument as a battle against the opposite side, and as a result take more and more extreme positions. Sometimes people are afraid to offer measured opinions because their own side will call them a traitor.
For example a politician may demonize drugs and suggest longer sentences for drug addicts, because taking a more balanced view will make him look like he supports drugs.
Some other examples of this fallacy are:
Either you are with us or against us.
Either we improve this law or everyone will suffer.
Either you go to church or you are a bad person.
Either you are a republican or a democrat.
To overcome it, remember that in reality things are rarely one-sided. Most of the time complex issues have costs and benefits. Optimizing for values often requires trade offs. To get the most accurate picture, you want to see flaws and advantages of both positions.
Just because you support one side of the with one group of people, doesn’t mean you have to automatically agree with everything that side says and reject the opposite side.