(1) Can good analogical inferences oppose each other?
(2) Must analogies meet some condition beyond real resemblance in order to be good?
I've suggested that we can call positions that answer Yes to the first question 'inclusivist', with 'exclusivist' for the No position, and that we can call positions that answer Yes to the second condition 'restrictivist', with 'generalist' for the No position. This gives us four combinations:
However, as I've also noted previously, there's reason to think that the exclusivist generalist category -- an account in which acceptable analogical inferences cannot come to conflicting conclusions but are based on nothing but resemblance -- is necessarily empty; that is, that it is impossible to hold such a position consistently. Inclusivist restrictivism seems possible, on the other hand, but it's difficult to think of any argument for it that would not be a better argument for another position; the restriction seems ad hoc because the most obvious reason for adding a restriction to analogical inference is to make good analogical arguments cohere. In any case, overwhelmingly, the two dominant accounts are inclusivist generalist (Hume is a good example) and exclusivist restrictivist (Mill is the obvious example).
The basic principle for inclusivist generalism is, in slogan form, that every resemblance affords a reason. But Mill does say things that are like this. For instance:
There can be no doubt that every such resemblance which can be pointed out between B and A, affords some degree of probability, beyond what would otherwise exist, in favor of the conclusion drawn from it....Every resemblance which can be shown to exist, affords ground for expecting an indefinite number of other resemblances; the particular resemblance sought will, therefore, be oftener found among things thus known to resemble, than among things between which we know of no resemblance.
On its own, this sounds very much like inclusivist generalism. However, Mill is presupposing a context; the first sentence does not say 'every resemblance' but 'every such resemblance'; Mill seems to take these claims to apply not to every resemblance but every resemblance of a relevant kind (namely, where we have causal information about how the properties we are talking about are related to each other). And Mill, of course, doesn't rule out the possibility that you can have apparently good analogical inferences that conflict; he just thinks that in such a case one of the inferences must be mischaracterizing the actual causal situation. This is clear enough from his account of the fallacy of false analogy. The quality of the analogical inference depends on the quality of prior causal inference. This contrasts sharply with Hume, for whom the quality of analogical inference is, in itself, completely independent of causal inferences. Hume, indeed, quite clearly thinks that analogical inference is more fundamental than causal inference.
So perhaps the distinction is due to different answers to the question of whether analogical inference depends on some more fundamental inference.