How literally do you take the phrase "Show, don't tell"?

(My comment is optional to read if you don't care about my motive for writing the post)

Personally, I suffer from the fact that I have to constantly rewrite my draft and remove explanations for the actions, feelings of the characters and ent. Something as ridiculous and simple as, "He was offended by her words, but she didn't want to mean it," might be deleted. It's like I'm forbidding the reader to understand my text and giving out crude descriptions, trying to tell the story through dialogues and silent actions. Is this correct? How do you find a balance in what to show and what (and by whom) to tell?