In English, the possessive adjective ‘my’ is essentially the same thing as the pronoun in genitive. In Latin, however, the possessive adjectives ‘meus’, etc. are not the pronouns in genitive form, but rather they act like all Latin adjectives, agreeing with the noun in gender, number, and case.
This cause me some confusion when translating, as in §158. II. 10., ‘Why were you injuring my horse?’, where it appears I have two options (the key giving the former):
︎ Cūr equō meō nocēbās? (1st person possessive adjective in dative)
? Cūr equō meī nocēbās? (1st person pronoun in genitive)
But if the horse belonged to Sextus, we would not use
Cūr equō Sextō nocēbās? (‘Sextus’ in dative, which makes no sense as it is not an adjective)
but instead
︎ Cūr equō Sextī nocēbās? (‘Sextus’ in genitive)
§98 does state that ‘the possessives … are declined like adjectives’, implying, perhaps, that using the adjective is the preferred construction. Is that the case? Or is there a choice between using the possessive adjective and the pronoun in genitive? If there is a choice: Is there a difference in meaning between the two?
︎ Cūr equō meō nocēbās? (1st person possessive adjective in dative)
? Cūr equō meī nocēbās? (1st person pronoun in genitive)
As far as Classical Latin is concerned, I believe only the first sentence is considered grammatical.
There is a possibility to use mei, tui, etc. instead of meus, tuus, etc. but then there is a change in meaning: timor meus “the fear I have of something” vs. timor mei “the fear of me, the fear people have of me” amor tuus “the love you feel” vs. amor tui “the love people feel towards you” cura vestra “the care you take of something” vs. cura vestri “the care people take of you”
As you can see this can only work with certain types of nouns (AG §348), such a distinction can not be made for a noun like equus.
Basically, mei (the genitive) is used for the objective genitive: amor mei “love of me” not “my love” and the partitive genitive: pars mei “part of me” or with verbs that take an object in the genitive: mei meministi “you remember me”; meus a um is used for possession: liber meus “my book”. Contrast pars mei “a part of me” and pars mea “my part”.