I'm looking for a word that means
someone (especially a boss) who is not pleased (with your work, attitude etc.) no matter how hard you try.
While not rude per se, the implication of the word is that there's no way around it. This person is not "hard to please". It's plain impossible to please this person. I'd say it's not rude but harsh to tell a boss he's unpleasable.
Oh ho! I have an idea. Most of the words suggested so far definitely sound negative, which is to be expected, because it is a negative thing to be difficult to please.
How about particular?
"She is very particular in her preferences."
To say that a person is particular means that he has exacting expectations. A person may take that as a compliment if they agree and do not feel they are being mocked. I would happily admit that in my writing I am very particular about my choice of words. If somebody said that I was very particular about the meals I was served, it wouldn't seem quite so complimentary. The word is a little more elastic in its connotation.
Hypercritical is the quality of always finding fault and never being pleased.
I think persnickety is a good word to use here. It means "overly particular" or "fussy" and has the added benefit of sounding like it might not be insulting.
Placare in Italian means to calm someone down, to make amends, to soothe. Look up the English definition, and there's no mention of a person who is never satisfied or pleased. So although the term, implacable, is indeed classy and sounds refined, technically, it's incorrect.
Vocubulary.com offers this example
An implacable person just can’t be appeased. If you really offended your best friend and tried every kind of apology but she refused to speak to you again, you could describe her as implacable.
To please, in Italian, is contentare, in my view, a more appropriate word would be: discontent (OED 1. The state or condition of being discontented; want of content; dissatisfaction of mind: the opposite of content or contentment) or malcontent, a chronically dissatisfied person
"fussy " is what you are looking for. Fussy means very careful or too careful about choosing or accepting things and hence hard to please. For example fussy eater are those who turn their noses up at most of the dishes you can serve. They rarely like something.
Or (with a nod to The Shawshank Redemption):
Although I've understood that you're searching for a not-too-harsh term, I'd still add stubborn to the list, because it hasn't been mentioned yet, and it appears that it can convey this meaning.
Obviously, not to be thrown like that to a touchy boss.
Fastidious might be the word for someone who is very hard to please.
I think fastidious can suit well?
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