Use of contractions in formal writing

Question

We were taught that we should not use contraction like she's or she'd in formal writing.

However, a newspaper editorial uses these. Is the above rule not widely accepted? Or newspaper editorials are not formal writings?

Here is from the New York Times editorial "Mrs. Clinton, Show Voters Those Transcripts".

Public interest in these speeches is legitimate, and it is the public — not the candidate — who decides how much disclosure is enough. By stonewalling on these transcripts Mrs. Clinton plays into the hands of those who say she's not trustworthy and makes her own rules. Most important, she is damaging her credibility among Democrats who are begging her to show them that she'd run an accountable and transparent White House.

Answer 1

I like what Lynn Gaertner-Johnston has said about contractions in her writing blog:

I use contractions to communicate a flowing, easy style. As a writer, I want you, the reader, to feel that I am talking with you and that the words come easily. I do not want to communicate formally with you.

^{(NOTE: That's just an excerpt; I recommend that you read the entire post.)}

In regards to your question, I wouldn't regard a newspaper editorial as "formal writing." Editorial pieces are voices of opinion, usually designed to get the reader to think, and perhaps be persuaded to share the same viewpoint. Judicious use of contractions is therefore both reasonable and acceptable.

Furthermore, don't take the "avoid contractions" guidance to an extreme. I might be inclined to use fewer contractions in, say, a scientific paper, but there are few places where one or two contractions couldn't be sprinkled in.