I'd like more time in which to read, which I suspect is the wish of most writers, but short stories give you a chance to read a complete tale in a short amount of time. I like the 1500 to 2000 words type of short story and these are the ones I write the most of, but flash fiction is something I've taken up comparatively recently.
I have some collections of short stories on my shelves (mainly by P.G. Wodehouse). One day I'd like at least one of my collections on that shelf.
As a writer, the other thing I like about short stories is I can write them reasonably quickly, submit them and generally know whether they're accepted or not before too long. If one place doesn't like a story, maybe somewhere else will.
Equally rejection means I get a chance to look at the story again. To date, every story where I took another look (and carried out another rewrite) improved it. I have had pieces rejected, rewrote the piece, re-submitted it to the place I had in mind for it and then had the story accepted. And knowing that rejection is never personal and it is a chance to review and improve the piece makes rejection much easier to handle. Given every writer needs to get used to rejection, this is no bad thing.