I disagree. What she means is they need to stop thinking about who will become the S-Class mage. She's talking about the fact that when they came to the island, they were focused on outdoing one another. Not as enemies, but as rivals. But with the threat in the island now, it's time to forget about "teams" and focus on Fairy Tail as a whole.
except, after the enemy showed up, they all totally stopped being rivals. They all started teaming up. There was never any need to shout to heavens the need for teamwork, because they were already doing it.
This only person who cares about becoming S-class now is Cana, the rest sensibly dropped it when Grimoire Hearts showed up. I don't know who Levy think's she's convincing, because Cana obviously didn't hear/care.