As we see from these excerpts from the text, Dummit and Foote are disciples of "new math," a doctrine discredited in the 70's. Too often, strange symbols and jargon take the place of clear English prose. Extraneous concepts like "sets"--much less "finite nilpotent groups" or "invariant factor decompositions" or "symmetric multilinear maps"--are merely obstacles to a student's understanding of algebra. Sadly, the authors, holed up in their ivory towers, have not yet learned these vital educational lessons.Well, of course! It's not good as a text for middle schoolers, because it was never supposed to be! (And it probably comes with a preface saying "this is a text for juniors and seniors in college majoring in math", or something like that; can anybody who has a copy of the book confirm this?)
I think it might be a parody. I hope it's a parody, of what someone who expected a middle school algebra text and got an abstract algebra text would say. And I think every mathematician has had that moment where they told someone they're taking "algebra" and people say "but didn't you learn that years ago?"
And the author makes a point, perhaps inadvertently - there is a time and a place for the precise language of higher-level mathematics, and middle school isn't it.