Short answer: the shiny and dull sides are created during manufacturing. In the final rolling step, two layers of foil are passed through the mill at the same time. The faces touching the polished steel rollers become shiny; the faces touching each other come out dull.
The finish is not a built-in cooking mode
The U.S. Department of Agriculture's Food Safety and Inspection Service notes that it does not matter which side contacts food. For ordinary household foil, the two finishes are not “hot side” and “cold side,” and one side is not intended to face the oven.
Rolling the sheets together helps manufacturers make extremely thin foil without tearing it. When the paired layers are separated, each sheet naturally has one polished face and one matte face.
Quick follow-ups
FAQ
Which side of aluminum foil should touch food?
For standard household foil, either side can contact food; the shiny/dull difference comes from manufacturing.
Does the shiny side reflect more heat?
The surfaces can have slightly different optical properties, but ordinary cooking instructions do not require choosing a side because of how the foil is manufactured.
Check the evidence
Sources
Sources are linked for verification. FactToon summarizes them in our own words and does not reproduce their articles or images.