4 ideas
A Sphere visits A Square in Flatland and, to prove it exists, passes through his plane, where it can only appear as a circle that grows from a point and then shrinks. The Square takes this for trickery and cannot grasp it until the Sphere lifts him bodily out of the plane into Spaceland. Once back home, he is imprisoned as a heretic by the Circles for preaching a third dimension.
A being that cannot perceive a higher dimension can still infer it by following the pattern of lower ones. A point extends into a line, a line into a square, and a square into a cube, so the next step can be worked out even though it cannot be pictured. The mechanism is to accept a structural pattern as evidence when direct intuition fails.
Once the Square has seen three dimensions, he reasons by analogy that a fourth and fifth must exist. The Sphere who enlightened him angrily rejects this and banishes him. Having transcended one limit of perception, a person tends to treat their new vantage point as the final truth and reenacts the same dismissal they once suffered.
In Flatland, rank is fixed by the number of sides a figure has: Isosceles triangles are laborers, Squares are professionals, and near-Circles are priests. Women are straight lines, denied education and treated as dangerous. Encoding status in body shape makes a social order look like a law of nature, which lets the ruling Circles use doctrine and the suppression of 'irregulars' to present contingent class and gender arrangements as physical necessity.