Nancy,
Although the topic of Alain's article was reviewing other's finished work, you raise good questions about self-critique. There are two distinct differences between the article and your post: First "other's" vs. your own and second "finished" output vs. the process of editing a batch of images, which I think of more as "inputs."
In regards to your first two questions, “Why do we make that decision, and do we make it in a systemic and reasoned matter?” I'm generally pretty bad and doing anything religiously, but one thing I try to do is rank my photos. Just the process of ranking with stars or whatever gets you thinking in a more structured way and critiquing a bit further than "Eewwww, that didn't work," or "Ooh, I like this one." It is equally important to define your ranking, much like Alain defined his pyramid. It doesn’t matter how you define it, just so long as you know what it means and it can be applied over an extended period, like your life!
For example, the difference between my 3 and 4 star rank is:
3. Has everything; meaningful style, artistically and technically good, wants to be printed
4. Image has a defining style; part of a Life’s Portfolio
So determining the difference between each level in my ranking system takes some thought and self-critique. Also note my criteria may be ambiguous or useless to others, but I know what I mean by "meaningful", "good", "wants to be printed", and "defining style."
Your third question, “Why did an image not work?” could if you like, be a specific step in your process. For example if you rank something below a certain level, force yourself to document the answer “why?” Maybe even in a EXIF field or specific keyword like X-Composition. Or put them in buckets to which you can apply a color label. So any image with “0” stars and a Red label means not used because of poor composition (or whatever criteria you come up with). I don't think many would always go to that trouble, but maybe during specific periods of someone's early development.
In regards to analyzing why we like someone else’s particular image, I find it interesting when I see an image with a particular style I am attracted to and it is different from my own. That is particularly important early on, and it is valuable in the development of my own style. For example, a few months ago Lula showcased Valerie Millett’s images, which I liked very much. I found it helpful to ask why and whether I want to incorporate some specific aspect of that style into my own. Or maybe a specific technique like using a neutral density filter. I don’t think that is copying; I think it is basic development and growth.
Dave