I never knew that "detaching" was a loaded term. I think the point is that we are looking at the same word and reading different things into it (?)
I think detaching on this forum means either:
* First meaning
: I do not discipline the child. I play, and laugh, offer a shoulder to cry on, help with homework, take the kid places, and cook and smile, BUT when the problem arises I allow her biological parent to work through the problems. (The reason for this might be the fact that the child was too old when you met him/her, and does not recognize you as a parental figure, while enjoys you as an adult friend).
* Second meaning:
I do not discipline the child, and I do not engage with a child, unless prompted by the child. I still cook, smile, wash the laundry, get the medicine, do everything I have to as a responsible adult has to do with a child in their care. The reason for this might be the fact that not only the child doesn't recognize you as a parent, but also shows you no respect for whatever reason (your husband is a hands off kind of dad that doesn't support you, and doesn't really parent while the child is aggressive towards you or your kids...)
* I suppose the third meaning will go right alone the lines of what you thought: I throw my hands up in the air and do bare minimum for this child, if that. The reasons for this is total frustration with the child who wants nothing to do with you in combination with unsupportive or clueless husband.
I understand the first two, and am I very certain that if it ever came to the third description I would probably not be in that relationship by that point. I would never advise or understand someone who simply goes about their life ignoring a child who is growing up right there in front of you.
I think when you say "not taking things personally", it's so hard sometimes... DSD and I get along fairly well, but when something comes up I am an emotional mess! And trust me, it's not because I don't care for this girl, or don't understand that she's been through very rough few years of divorce. It's just because I care, and because she is not my child, it's so much harder for me to believe that she didn't mean things she said or did out of anger, kwim? Don't get me wrong, I don't agree with people mistreating kids (or "detaching" in a way you describe), all I'm saying is that step parenting doesn't seem to lend itself to "not taking things personally".
I don't know if I succeeded, but I tried. My point was that I think we understand the word differently, and I would never advocate "detachment" in the sense you described.