the.com/false dichotomy

means A false dichotomy frames a situation as only two possible options when more actually exist, forcing a choice between extremes that ignores the middle ground.

from The pieces come from different places: 'dichotomy' traces to Greek dicha ('in two') plus temnein ('to cut'), originally a neutral term for any division into two parts, used in logic and botany alike. 'False' is just the Latin-rooted word for untrue, bolted on in modern usage. The phrase itself isn't ancient — it's a 20th-century term from logic and rhetoric, coined to name a recognized fallacy: the rigged either/or. So the word's root is an honest, old idea of 'cutting into two,' but the compound phrase is a newer label for the dishonest move of pretending a cut is the only one available.