1620s, from in- (1) "not" + expressible (see express (v.)). Inexpressibles "trousers" is from 1790. Related: Inexpressibly.
I have retain'd the word BREECHES, as they are known by no other name amongst country folk.--The change from vulgarity to refinement, in cities and towns, has introduced other appellations; there they are generally called SMALL CLOTHES, but some ladies of high rank and extreme delicacy call them INEXPRESSIBLES. [footnote in "Poems Miscellaneous and Humorous," by Edward Nairne, Canterbury, 1791]
Inexpressibles is the earliest recorded and thus seems to have begotten the trend: Unmentionables (1806); indispensibles (1820); ineffables (1823); unutterables (1826); innominables (1827); and inexplicables (1829) followed.