People like to say that but it's never been explained to my satisfaction. Spaces are twice as wide in a monospace font. Why would you use more spaces when and only when you have a longer space?
I've also wondered this. Referring to this mock-up[1], I have the same monospace text with single vs double spaces after sentences, and proportional font with single vs double. The usual argument is that #2 is better than #1 (for mono), but #3 is better than #4 (for proportional). It feels like an inconsistency in the preference, and (as you pointed out) the reasoning doesn't make sense.
No, an em-width space between sentences with either half-em or third-em width space between words was typesettig convention for a long time before typewriters, and is where the triple (later double) spacing in typewritten manuscript convention came from.
Typesetting convention evolved to narrower and eventually mostly settled on equal-to-interword spacing after that typewriter convention evolved from earlier typesetting convention.
In short, wider sentence spacing goes back to the first English standards of the eighteenth century – including the first nine editions of the Chicago Manual of Style, and even the tenth still had it as an en-space – and only really started falling out of favour in the twenties. Typewriters had limited effect, but the automated typesetters that suceeded them were actually what killed it off, to simplify the programming.
I typically do still type a single space, but I take full advantage of my preferred TeX flavour's (ConTeXt) automatic conversion to wider spaces. One successful, post-education convert here!
EDIT: For completeness, here is that same text with an extra space: "I live in the U.S. I am happy." -- see how much easier that is to read? Sure, it's not that big a deal, but it's definitely kind to the reader.
I live in the U.S. I am happy.
I live in the U.S. I am happy.Full stops aren't generally used in abbreviations here, Mx Cryptonector.
Though there's a more recent trend to write "Nato" rather than NATO, which annoys me for the inconsistency that arises. Plenty of people pronounce VAT as one word, or PAYE, but these are usually left in capitals.
[0] https://www.theguardian.com/guardian-observer-style-guide-a
This convention started with typewriters, and typesetters (e.g. my parents) will tell you that it is only considered correct in monospace fonts. This is also why HTML takes the liberty of reducing whitespace down to a single space character unless you go out of your way to use an .