Origin of the word "delete"

delete "destroy, eradicate," 1530s, from Latin deletus, past participle of delere "destroy, blot out, efface," from delevi, originally perfective tense of delinere "to daub, erase by smudging" (as of the wax on a writing table), from de "from, away" (see de-) + linere "to smear, wipe," from PIE root *(s)lei- "slime, slimy, sticky" (see slime (n.)). In English, specifically in reference to written matter from c. 1600. Related: Deleted; deleting.

This gives a clue as to why a latin word was used. 'Deleting' was something that people did with their writing, to erase words. In the 1530s in England, only scholars would have the ability to write, and Latin was generally the language of scholarship in England.

I can't imagine why the other languages forgot this word though.

The OED's earliest citation (which it admits may be questionable and isn't included in other etymologies that I've looked at) is from 1495 from a translation of Bartholomeus Anglicus's De proprietatibus rerum, a translation of a Latin text into English (they don't list the translator): "1495 Barth. De P.R. (W. de W.) iv. iii. 82 Drinesse dystroyeth bodyes that haue soules, so he dyssoluyth and delyteth the kynde naturall spyrytes that ben of mayst smoke.". Hence, if this is the source, it probably came directly from Latin into English.

Citations from the 1530s and 1540s are from the acts and declarations of Henry VIII, and therefore the origin of the word is harder to guess.

Source: "delete, v." OED Online. Oxford University Press, September 2019. Web. 14 November 2019.

No idea about other languages, and they're off topic here, but it's worth noting that French has an adjective délétère cognate with English "deleterious" attested as early as 1370.