Analogy—the drawing out of some similar feature between otherwise different phenomena—is not just the central tool of academic philosophy, it's the way rational beings think about complex matters. It is for this reason that Funes the Memorious' inability to draw abstract connections between distinct memories renders the man incapable of rational thought.
That's why that commonplace response of moral outrage: “Did you really just compare X with Y” constitutes such a grave obstacle to clear thinking.
Analogy does not mean the similarity of two things, but the similarity or sameness of two relations. There must be more than two things to give rise to two relations: there must be at least three; and in most cases there are four. Thus A may be like B, but there is no analogy between A and B: it is an abuse of the word to speak so, and it leads to much confusion of thought. If A has the same relation to B which C has to D, then there is an analogy. If the first relation be well known, it may serve to explain the second, which is less known; and the transfer of name from one of the terms in the relation best known to its corresponding term in the other, causes no confusion, but, on the contrary, tends to remind us of the similarity that exists in these relations; and so assists the mind instead of misleading it.