Two reasons why you shouldn't double space

1. It's anachronistic
Unless you're working on a typewriter, there is absolutely no need to smack that space bar more than once. Don't take my word for it – behold the wisdom of Robert Bringhurst, from the Elements of Typographic Style:

“In the 19th century, which was a dark and inflationary age in typography and type design, many compositors were encouraged to stuff extra space between sentences. Generations of 20th century typists were then taught to do the same, by hitting the spacebar twice after every period [full stop]. Your typing as well as your typesetting will benefit from unlearning this quaint Victorian habit. As a general rule, no more than a single space is required after a period, colon or any other mark of punctuation.”

2. It really gets my goat
And you wouldn't like me when I've got my goat.