To become the strongest
The students were starting to leave the room one by one. It was their day off and they didn't want to hang around in the assemble hall any longer than they needed to. Most of them were leaving with smiles on their faces, excited for the upcoming event.
With Jack mentioning and informing the students of his plans to be at the Inter military base event. They were now eager to impress him, and wanted to start practising right away. If Jack was to offer them an invitation to join his family it would be a shortcut to the top.
Usually, unless one was extremely talented they would have to build a reputation for themselves from their own factions and work their way up. Nearly everyone, who wished to become a traveller had a goal of joining the big four.
Even if you created your own faction, it was beneficial to work under one of the big four, mainly for protection from the others.