The story
From pig (“animal of the family Suidae, especially the domesticated animal Sus domesticus; oblong block of cast metal (iron or lead)”) + iron. It appears that in early use sow was used to refer to larger blocks of smelted metal and pig smaller ones. From the 17th century, the words were adapted to newer methods of iron smelting, with pig used to describe blocks formed from molten iron served from the central channel (runner) of a pig bed which were said to resemble a litter of piglets nursing from a sow.
Etymology from Wiktionary, CC BY-SA 4.0.