The passage mainly argues

that every flat map must distort the round Earth, trading one accuracy for another (The passage argues that flattening a sphere forces distortion, so each map trades one kind of accuracy for another.)

What does the Mercator projection keep correct?

The shapes of countries and the directions between them (The text says Mercator 'keeps the shapes of countries and the directions between them correct'.)

Why does the passage say a wise reader asks what a map 'traded away'?

Because each flat map gives up one kind of accuracy to keep another (Since a flat map must distort something, no map is simply right; each keeps one accuracy by giving up another.)

In this passage, to 'distort' shapes means to

show them in a false, stretched form (Set against being 'honest', to distort is to show something in a false, stretched form.)

Why Every Flat Map Lies: Level 3 Reading Comprehension Questions

A globe shows the Earth truthfully, but a globe is hard to carry and hard to print in a book. So mapmakers flatten the round Earth onto a flat sheet. The trouble is that a sphere cannot be flattened without stretching some parts of it. Every flat map, therefore, is wrong in some way. The only choice is which error to accept.

One famous world map, the Mercator projection, keeps the shapes of countries and the directions between them correct, which made it useful for sailors steering a course. But it pays for this by stretching areas near the top and bottom of the map. Lands close to the poles look far larger than they really are. On such a map, Greenland can appear as big as Africa, though Africa is many times its size.

This does not make the map useless; it makes it a tool with a known bias. A map that is honest about distances may distort shapes instead. The wise reader asks not 'Is this map right?' but 'What does this map get right, and what has it traded away?'

Comprehension questions