The Arche persona symbolizes a part of a person that they do not fully understand and that is difficult for them to accept, similar to the function of shadows in Persona 4.
From dialogue it appears that the cause of Akihiko's Arche is his place in the group and an apparent dogma for friends in his past. Akihiko feels distant to those younger than him and that causes him to feel inadequate. Accordingly, the pre-battle dialogue options are "I don’t know what to say" and "You are enough".
The stats of Arche-Polydeuces mirror those of Polydeuces, which also symbolizes its shadowy, opposite nature.