The term “under-privileged” was current in an American middle-class vocabulary at this time [during the Cold War] as a euphemistic substitute for the stark word “unprivileged”. In American mouths “under-privileged” was a less unpalatable term, because it suggested that the difference of level was not very great; that its elimination was already on the agenda; and that “privilege” itself was, not an abuse which ought to be abolished, but an objective which could and should be attained by Everyman. “Under-privileged” was, however, a flagrantly illogical term, considering that the conferment of a favoured minority’s privileges on members of a depressed class must still leave a residual depressed majority on an implicitly unacceptable lower level or, alternatively, must abolish “privilege” itself […]. A privilege that is shared by everybody, or even only by a majority, is a contradictio in adjecto, and a psychologist would perhaps have deduced from this revealingly illogical American euphemism the existence of an unresolved conflict in the souls of middle-class Americans between a natural human desire to retain the relatively high standard of living which they were now enjoying as members of an invidiously privileged minority and a conscience which must reproach itself so long as this stigma of privilege was […] justifiable [for them] in virtue of its being a natural and normal human right that, by implication, must be Everyman’s due.
Americans are masters of euphemism. (On the other hand, you see the word INCONTINENCE in large letters above shelves in pharmacies.)
The OED does not help us in this case.
“underˈprivileged, adj. (and n.)
1. Less privileged than others; spec. experiencing a standard of living which falls short of an accepted norm, socially disadvantaged. Chiefly applied to persons.
2. absol. as n. with the.”
The first definition implies degrees of privilege. If the gap is wide, the less privileged person is underprivileged, which does not work. One can then at best object to a person being overprivileged.
And since this word implies that the other is underprivileged it, too, must be rejected. The word makes moral sense only if the “accepted norm” is that of homo sapiens in relation to other species. A human specimen could then be underprivileged.
And the second definition is not really an absolute.
The first use known to OED is by James Barnes in A Princetonian, A Story of Undergraduate Life at the College of New Jersey, New York, G. P. Putnam’s Sons, 1896. “It was very quiet in the little square that was filled with nurse-maids and children moving about inside the railings – several little underprivileged ones peering in at them from the outside.”
A Study of History, Vol VIII, OUP, 1954 (footnote)