"saddle leather or binding made from the skin of a pig," 1855, from pig (n.1) + skin (n.). Hence, in slang, "a saddle." As slang for "a football" by 1894.
Entries linking to pigskin
pig n.1
Middle English pigge "a young pig" (mid-13c., late 12c. as a surname), probably from Old English *picg, found in compounds, but, like dog, its further etymology unknown. The older general word for adults was swine, if female, sow, if male, boar. Apparently related to Low German bigge, Dutch big ("but the phonology is difficult" -- OED).
By early 14c. pig was used of a swine or hog regardless of age or sex. Applied to persons, usually in contempt, since 1540s; the derogatory meaning "police officer" has been in underworld slang at least since 1811.
The pigs frisked my panney, and nailed my screws; the officers searched my house, and seized my picklock keys. ["Dictionary of Buckish Slang, University Wit and Pickpocket Eloquence," London, 1811]
Another Old English word for the animal was fearh, which is related to furh "furrow," from PIE *perk- "dig, furrow" (source also of Latin porcus "pig," see pork). "This reflects a widespread IE tendency to name animals from typical attributes or activities" [Lass].
Synonyms grunter, porker are from sailors' and fishermen's euphemistic avoidance of uttering the word pig at sea, a superstition perhaps based on the fate of the Gadarene swine, who drowned. The image of a pig in a poke is attested from late 14c. (see poke (n.1)). Flying pigs as a type of something unreal is from 1610s.
skin n.
c. 1200, "animal hide" (usually dressed and tanned), from Old Norse skinn "animal hide, fur," from Proto-Germanic *skinth- (source also of rare Old English scinn, Old High German scinten, German schinden "to flay, skin;" German dialectal schind "skin of a fruit," Flemish schinde "bark"), from PIE *sken- "to peel off, flay" (source also of Breton scant "scale of a fish," Irish scainim "I tear, I burst"), extended form of root *sek- "to cut."
The usual Anglo-Saxon word is hide (n.1). The meaning "epidermis of a living animal or person" is attested from early 14c.; extended to fruits, vegetables, etc. late 14c. Jazz slang sense of "drum" is from 1927. As short for skinhead from 1970. As an adjective, it formerly had a slang sense of "cheating" (1868, compare the verb); that of "pornographic" is attested from 1968. Skin deep "superficial, not deeper than the thickness of the skin" (also literally, of wounds, etc.) is attested by 1610s:
All the carnall beauty of my wife, Is but skin-deep.
[Sir Thomas Overbury, "A Wife," 1613; the poem was a main motive for his murder]
The skin of one's teeth as the narrowest of margins is attested from 1550s in the Geneva Bible, a literal translation of the Hebrew text in Job xix.20. To get under (someone's) skin "annoy" is from 1896. Skin graft is from 1871. Skin merchant "recruiting officer" is from 1792 (the older sense is "dealer in hides"). Skin and bone as a description of emaciation or extreme leanness is in Middle English:
Ful of fleissche Y was to fele, Now ... Me is lefte But skyn & boon. [hymn, c. 1430]