Consider a language where each noun belongs to a multitude of binary categories, e.g. masculine vs. feminine, human vs. non-human, animate vs. inanimate, older vs. younger, upper social class or lower social class. Some of these are absolute, e.g. human vs. non-human, but some are mutable: older vs. younger is dependent on the other nouns involved.
Now, most verbs have an associated category, and the direct form generally prefers the older, the animate, etc, [...] noun as the subject. Feminine and masculine, however, do not form a typical hierarchy, and both of them have verbs where 'direct' assumes one or the other gender.
A few verbs have two categories - breast-feed, for instance, assumes older and female, teach assumes older and higher social class. Resolving a situation where both participants fail to have both requires some special morphology.
The exact function of the inverse in such a situation is not a thing I care to think about right now, and it can safely be left as an exercise for the diligent reader.
However, a situation that will appear often enough is that both arguments have the same properties - both are animate, both are human, both are masculine, etc. In this situation, a different system sets in: the highest ranked class in which the subject "wins" gets a class-specific marker present on the verb; however, if the subject does not win, the verb is detransitivized, and the object gets demoted to an oblique position.