Per Etymonline:
italic 1610s (adj.), 1670s (n.) "italic type," from Latin italicus "Italian"; so called because it was introduced in 1501 by Aldus Manutius, printer of Venice (who also gave his name to Aldine), and first used in an edition of Virgil dedicated to Italy. Earlier (1570s) the word was used for the plain, sloping style of handwriting, as opposed to Gothic.
Per Fonts.com
Aldus Manutius’ italic type evolved from a writing style that had become popular by the end of the 15th century with the educated class, including professional scribes, in southern Italy. Its heritage can be traced back to Niccolo de Niccoli, an Italian scholar of the early 15th century. De Niccoli started to oblique and add flourishes to his letters when he wished to write in a faster more relaxed fashion than usual. By mid-century, other scholars began to imitate his writing. Manutius commissioned typeface designer Francesco Griffo da Bologna to develop a cursive type for a new series of small books he was planning to produce. ...[O]ther printers felt obliged to produce their own books in this new typestyle. The problem was that Manutius would not sell his new fonts to the competition. So Manutius’ contemporaries did what has become a common practice in the history of type design – they copied the designs they could not buy. Not wishing to call attention to their plagiarism, but still needing to give the new offering a name, Manutius’ competitors chose “italic,” after Italy, the country where it originated.
Here is a picture of Niccolo's writing:
Compare to the norm before Niccolo:
Close up: see the words that comes in, of, to th(?) pharisees and note the predominantly vertical strokes.
This is from a work made in the middle of the fourteenth century in Italy (from a book of astrology, British Library):