EcoGeoFemme recently mentioned constructive criticism in writing and how she's relatively thick-skinned. I must have skin like a rhinosaurus in this way, because I've been taught from the very beginning that you should always have someone else look over your work. Likewise, it'll make things infinitely better if you step away from what you're writing, wait a couple days, and re-read it (something I wasn't able to do for my thesis, which was the worse for it...I'll have to discuss that later). So I've always had someone pick apart my writing.
It's a lot easier to critique someone's writing than do some other form of constructive criticism. First, it's written. Instead of saying "maybe you should do it this way," you can let your red pen do the work in a relatively non-judgemental way (as long as you go easy on the angry underlines and exclamation points, which can be tempting).
Like EcoGeoFemme, I am familiar with workshopping, in which your peers go through and comment on not just the form (relatively easy), but also the content of something that's intensely personal. And I found myself frustrated by people who would write some sort of vague "looks good!". Not helpful, people! My writing was helped immensely by a very picky science professor who covered my papers in red ink, and I return the favor for my friends' papers and that of the students I've TA'd. Heck, I fix spelling/grammar mistakes on labs.
I don't always agree with the people who edit my stuff. I have long, drawn out arguments with my SO, who has a different writing style. I have the option of ignoring suggestions. But if I don't have the suggestion, I may miss something I hadn't noticed. Like, oh, writing "pubic" instead of "public" on a notice that's getting sent to a community that may not particularly appreciate what my company is doing.