Well, because it's a generalised descriptor and any form of writing which uses ligatures to increase speed is "cursive" by definition - including Greek, various South Asian scripts - and Chinese for that matter. We know what we generally mean by it: a distinctively American form of handwriting deriving from 19th century business styles and with its deep roots in Spencerian, but really all it means is "joined-up writing". This has been bugging me for a while!
Incidentally, ignoring all that, where do you think the division between business writing and American cursive lies? It's not at all obvious to me.