When shape names are first introduced, many kids will flip out if you suggest a given polygon can be multiple things at once. So they define the shapes (square, rectangle, rhombus, parallelogram, trapezoid, etc.) so they are mutually exclusive, with categories like quadrilateral as residual categories. You can tell who is doing AoPS/Beast Academy because they argue based on the standard definitions, whereas the teacher will insist on the curricular definition or on the “most specific answer.”
Another classic is “how many roots does a parabola with real coefficients have?” The answer is always two by the FTA, but the textbook Algebra 1 answer is zero, one, or two because they haven’t covered complex numbers yet.
Another classic is “how many roots does a parabola with real coefficients have?” The answer is always two by the FTA, but the textbook Algebra 1 answer is zero, one, or two because they haven’t covered complex numbers yet.