The Sahara is the desert. Endless dunes, blistering heat, camel trains to the horizon. When someone says 'largest desert on Earth', your brain fills in the Sahara before they finish the sentence, and it is genuinely vast, roughly the size of the United States.
A desert is defined by how little precipitation it gets, not by sand or heat. By that definition, the largest desert on the planet is Antarctica, a frozen continent that receives so little snowfall that its interior is technically one of the driest places on Earth. Antarctica covers about 14 million square kilometres. The Sahara covers about 9 million. The Arctic also outranks the Sahara on the same logic. So the Sahara is the largest hot desert, which is a real and respectable title, just not the one everyone gives it. The mental image of a desert as a golden, sun-baked wasteland is the whole problem. Swap 'sand' for 'dry' in your head and the leaderboard flips to a place covered in two kilometres of ice.