Why was the Mercator map invented?
For navigation. Before 1569, sailors could not easily chart a constant compass course on paper: Mercator's projection makes any straight line on the map a line of constant true bearing (a rhumb line). It solved a deadly real-world problem — at the price of inflating high-latitude land.
Is the Mercator map wrong?
Not for its job. Mercator is a distortion, not an error — every flat map distorts something. It distorts area badly, so it misleads anyone comparing country sizes: Africa is about 14 times larger than Greenland, not smaller. For that question, an equal-area map like Equal Earth is correct.
How much does Mercator distort area?
Inflation equals 1/cos(latitude)². At 30° it is ~1.3×, at 45° ~2×, at 60° ~4×, at 70° ~8.5× and at 80° ~33×. This is why equatorial countries look real and northern ones blow up.