Terminological inexactitude is a phrase introduced in 1906 by British politician (later Prime Minister) Winston Churchill. Today, it is used as a euphemism or circumlocution meaning a lie or untruth.
Churchill first used the phrase during the 1906 election. Following the election, speaking in the House of Commons on 22 February 1906 as Under-Secretary of the Colonial Office, he repeated what he had said during the campaign:
The conditions of the Transvaal ordinance ... cannot in the opinion of His Majesty's Government be classified as slavery; at least, that word in its full sense could not be applied without a risk of terminological inexactitude.
It seems this first usage was strictly literal, merely a roundabout way of referring to inexact or inaccurate terminology. But it was soon interpreted or taken up as a euphemism for an outright lie. To accuse another member in the House of Commons of lying is unparliamentary, so a way of implying that without saying it was very useful.