[A recent] WOTD discusses the suffix -ly and uses the word thirdly as an example. This touched a nerve. In my undergraduate days, I had an English professor redline that word out of a paper I wrote, along with the terms (equally offensive to him) firstly, secondly, and lastly. He wrote next to each deletion the comment, "no such word" in bold, red ink. I've spent the last 15 years or so...editing memos and business letters to remove this use of "-ly" as a means of introducing a series of examples or arguments....After all this effort, is there really nothing wrong with firstly, secondly, or lastly?
As with so many aspects of language, when it comes to enumerative adverbs, people tend to dogmatism. At the extremes, we have on one side your English professor claiming that firstly is not a word, and on the other, a mid-19th-century writer on usage who insisted that first is not an adverb (George Washington Moon, The Dean's English). As any modern dictionary will show, they were both wrong.

I'm afraid your teacher undermined his position by carrying it to such an absurd extreme. Firstly and thirdly have been part of the English language since the early 16th century. Secondly is even older, having appeared (in the Middle English form "secundelich") in Chaucer's narrative poem Troilus and Criseyde in the 1370s. These terms, including lastly, are certainly not "nonwords." Almost a half century ago, A Dictionary of Contemporary American Usage pointed out that "Many speakers begin with 'first' and then go on with 'secondly, thirdly' and so on. But 'firstly' is respectable English" (Evans and Evans, 1957).

The firstly crowd, however, is equally mistaken if they fancy that their enumerations are made more proper by avoiding first, second, third, etc. Enumerative adverbs without -ly have an even longer heritage, with first going back to around 1200, and second found in John Wycliffe's 1382 translation of the Bible.

Most usage authorities during the last half century, from Wilson Follett and Jacques Barzun (Modern American Usage, 1966) to The New York Times Manual of Style and Usage (1999), have pretty much agreed with your professor and recommended "No -ly," on the grounds that the extra syllable is...well...extra. A current, highly regarded usage book that remains neutral, acknowledging (with many citations) the historicity of both varieties, is Merriam Webster's Dictionary of English Usage.

Granted that neither first nor firstly is a hanging offense, even professional lexicographers may have a personal preference. I happen to think your repeated deletions of -ly represent time well spent. Partly this is a matter of consistency: I can't imagine anyone saying "eleventhly" or "seventeenthly"--and even those who do use "firstly" in enumerations would never use it in any other adverbial context ("The Smyths arrived at the party firstly and left lastly?"). But perhaps another reason to avoid firstly and secondly is that they resemble hypercorrections--inappropriate forms substituted for perfectly good ones, out of a desire to sound especially correct.

Ultimately, the choice is one of style: Since first is a perfectly good adverb just as it stands, there is no need for the -ly. As E.B. White put it in the chapter he contributed to Strunk and White's The Elements of Style (1959): "Do not dress words up by adding 'ly' to them, as though putting a hat on a horse."