When is it prudent to argue against a suggested revision to a journal paper? Most journals have a peer review process, where there are several rounds of reviews and modifications over a single paper.

In my particular case, one of these reviews was, in my opinion, a bit over the top. In this case, the reviewer asked me to expand a set of equations that are explained in any undergrad numerical analysis book. It even has a very well described Wikipedia page. And the set of equations took an entire page of my paper.

Yet, my PI at the moment told me it was just better to comply and get the paper ready (it had already been accepted subject to these changes). 

My new PI told me it seemed wrong to him, since it is a very basic set of equations and the fact that one reviewer is not familiarized with it, is not an excuse to break the rhythm of the paper, since suddenly a whole page of equations can do that for you in a paper.

He told me he would have fought it back. 

What is the overall opinion in different fields with respect to this?
From what I know (I am a mathematician with some publishing experience), it is perfectly okay to argue against a referee's demand, as soon as 


you do it politely, and you explain your arguments in a non-conflictual way;
you are ready to delay the final acceptance of your paper;
you are ready to either ultimately  accept the demand if the referee does not change her mind and the editor backs her up, or to get your paper ultimately rejected.


In the case you describe, I do not think that explaining your point of view would have turn the editor's mind right away. In a similar situation (a referee asked for some terminology to be changed into something more standard), with my coauthor we argued with success (our argument was that to date, no terminology existed for what we discussed, let alone standard terminology).

Added in edit: I forgot an important point; in many situation, including yours, you can find a middle ground that may be considered an acceptable answer to her query by the referee, and that avoid departing too much from your initial intention. For example, in your case, you can propose to add a precise reference giving the derivation.