Why do we use rectangular paper rather than square paper?

The most likely reason we use rectangular paper goes back to the early days of paper production.

Until the start of 19th Century, paper was made by hand, dipping a mold (mould if you prefer the British spelling) into a large vat containing beaten pulp in suspension.

Early papermakers found it much easier to control rectangular molds than square ones. The rectangular size tradition continued after the process was mechanized in the 19th Century, and mechanical blades were used to cut the rolls of paper for the commercial market.

Tradition has kept the shape rectangular.

Article by Institute of Paper Science & Technology