The subjective and objective genitive case uses can be tricky. These two genitive case uses both involve a noun in the genitive paired with a noun that has a verbal idea like “love.” “Love” can be a noun or a verb. More often than not, however, the noun and the verb are closely related, but not identical. Take for instance the word “growth.” It is a noun, but it is clearly related to the verb “grow.”

The terms “subjective” and “objective” have something to do with verbs as well, don't they? Subjects perform actions, objects receive them. Consider this sentence:

Augur mī tum avium in caelī spectā bat. (The augur was watching the movement of birds in the sky.)

The genitive phrase is mī tum avium (“the movement of birds”). The birds don't own movement. Movement is not a quantity of birds. But the birds are moving — they are the subjects of the verbal idea of the noun mī tum (“movement”). Avium, then, is a subjective genitive.

Now we can turn this around. Here is another sentence:

Odium bellī in oppidī erat magnum. (The hatred of war in the town was great.)

Odium (“hatred”) has an obvious link to the verb “to hate.” But is the war doing the hating, or is war what is hated? In this example, the word in the genitive is receiving the action. That is to say, it is the object. Bellī, then, is an objective genitive.