Actually neither does the MC get a persona by facing his inner self.
Both him and the adachi (don't read this people who haven't played the game, but I don't know how to do spoiler tags), were given the power of persona by Izanami, since they both represented the World Arcana, thus they had innate persona powers within them. Remember the hand shacking scene on the beginning of the game? That's what activated the persona inside the MC. For adachi was pretty much the same, but Izanami saw in both the MC and Adachi conflicting personalities that would lead to the strife that followed. She didn't care about the outcome nor about the protagonists, she just wanted to see the conflict of human behaviours.
Hope you get to do a second playthrough soon, and i'm glad you liked the game ;)
Current PC Build
CPU - i7 8700K 3.7 GHz (4.7 GHz turbo) 6 cores OC'd to 5.2 GHz with Watercooling (Hydro Series H110i) | MB - Gigabyte Z370 HD3P ATX | Gigabyte GTX 1080ti Gaming OC BLACK 11G (1657 MHz Boost Core / 11010 MHz Memory) | RAM - Corsair DIMM 32GB DDR4, 2400 MHz | PSU - Corsair CX650M (80+ Bronze) 650W | Audio - Asus Essence STX II 7.1 | Monitor - Samsung U28E590D 4K UHD, Freesync, 1 ms, 60 Hz, 28"
