I remember when I first read this and thought, "Thank goodness. I am meant to be a copyeditor!"
I didn't read this bit of advice until I had been employed in publishing for nearly two years, frighteningly enough. But I clearly remember the wave of relief that washed over me when I realized that I was the luckiest person alive: I had the natural skills to succeed in my chosen career.
There is plenty you can learn about a job, especially when that job is copyediting or proofreading, but the instinct to look up a word you are unsure of is not a learned skill. You can't learn an instinct. You can hone an instinct . . . but, whatever. I'm getting picky. The point is, there are plenty of people who who see "non-symmetrical" printed somewhere and take that hyphen at face value. Me? That's something I actually looked up today while I was working. According to my trusty dictionary, that hyphen is incorrect.
Obviously, we all know of Merriam-Webster because of Noah Webster, the father of the American English dictionary. (You don't? Well, that's another topic for another time.) But what made Merriam-Webster's dictionary the definitive dictionary of the modern era? Because it really is the definitive source for spelling these days. Especially in publishing.
The Chicago Manual of Style uses Webster as its go-to for all spellings, and almost all publishing houses use CMS as their go-to for style. Here's what CMS has to say about Webster:
7.1 Recommended dictionaries.
For general matters of spelling, Chicago recommends using Webster's Third New International Dictionary and its chief abridgment, Merriam-Webster's Collegiate Dictionary (referred to below as Webster) in its latest edition.1 If more than one spelling is given, or more than one form of the plural (see 7.7), Chicago normally opts for the first form listed, thus aiding consistency. If, as occasionally happens, the Collegiate disagrees with the Third International, the Collegiate should be followed, since it represents the latest lexical research.**
The Scripps National Spelling Bee also bows to the lexicographical genius of Webster, using it as their official dictionary.
I guess the overall point is this: If you're looking to invest in a new dictionary, especially if you're employed in publishing or hope to be employed in publishing, you can't go wrong purchasing Webster. And don't be afraid to use your dictionary. Those of us in publishing, be it writing, editing, or proofreading, did not get here by being dumb. It's easy to think, "I am a champion speller; I know that non-symmetrical is a hyphenated compound." But it takes guts to admit that you could be wrong, and pick up that dictionary.
Luckily, I have lots and lots and lots of guts.
*Karen Judd, Copyediting: A Practical Guide (New York: Thomson Crisp, 2001), p. 15.
**Chicago Manual of Style, 15th ed., 7.1.