Learn Italian: La gloria è diventata un'ossessione per lui. - Glory has become an obsession for him.

In Italian, abstract nouns like gloria (glory) require a definite article when discussed as a general concept, unlike in English where we often drop it.

Doesn't 'diventare' have a direct object here ('un'ossessione')? Why does it take 'essere'?

It looks like a direct object, but diventare (to become) is a copular verb. It connects the subject to a new state or identity rather than acting upon an object. Verbs expressing a change of state always take essere in compound tenses, which is why the past participle agrees with the feminine subject and becomes diventata.

How does the nuance change if I rewrite this as 'Gli è diventata un'ossessione'?

Both are grammatically correct, but using the stressed pronoun phrase per lui instead of the unstressed indirect object pronoun gli adds emphasis. It highlights that glory has become an obsession specifically for him, subtly implying a contrast with how others might view it.