The protagonist and Morgana the cat have some prior relationship. In the scene when he's walking in the subway, you can see that he's carrying her in his backpack.
So I have two theories about this:
1. The protagonist is the owner of the magical shape shifting cat Morgana and they've been partners in crime for awhile.
2. Due to some prior events the protagonist is forced to carry Morgana around sort of like the relationship between Midna and Link in Twilight Princess.
Btw, I don't want to take credit discovering this. I found this out through googling Persona 5 trailer analyses videos.