"The boy will become a man."
Translation:Το αγόρι θα γίνει άντρας.
Because this sentence doesn't use the accusative case.
είμαι "to be" and γίνομαι "to become" use the nominative case for both the subject and the complement.
Αυτός είναι δάσκαλος και θα γίνει καθηγητής "He (nom.) is a teacher (nom.) and he will become a professor (nom.)"
I knew this was the case for είμαι, but I didn't know about γίνομαι. Thanks for the clarification.
The indefinite article is dropped and implied, because you're talkng about something that could only be one. The boy could only become one man, not two. ^.^ Also, it's a phrase with "general" meaning. ^.^