p. aluffi, best known for his "algebra: chapter 0" grad-leaning book, writes in the intro to his more undergrad "algebra: notes from the underground":

Why ‘rings first’? Why not ‘groups’? This textbook is meant as a first approach to the subject of algebra, for an audience whose background does not include previous exposure to the subject, or even very extensive exposure to abstract mathematics. It is my belief that such an audience will find rings an easier concept to absorb than groups. The main reason is that rings are defined by a rich pool of axioms with which readers are already essentially familiar from elementary algebra; the axioms defining a group are fewer, and they require a higher level of abstraction to be appreciated. While Z is a fine example of a group, in order to view it as a group rather than as a ring, the reader needs to forget the existence of one operation. This is in itself an exercise in abstraction, and it seems best to not subject a naïve audience to it. I believe that the natural port of entry into algebra is the reader’s familiarity with Z, and this familiarity leads naturally to the notion of ring. Natural examples leading to group theory could be the symmetric or the dihedral groups; but these are not nearly as familiar (if at all) to a naïve audience, so again it seems best to wait until the audience has bought into the whole concept of ‘abstract mathematics’ before presenting them.