Mage is represented in the opening and their introduction song by a snake. One common symbolism of snakes is for the underworld. He and the others are devils.
Shiki is represented in the opening and their introduction song by a crow. A crow has black wings and Shiki is a Fallen Angel, and has black wings. Also, unlike the others' animal symbols, his is the only one to actually have wings — unlike the others who can levitate, Shiki uses his wings.
Why is Shiki the most antagonistic to Roen? In Episode 7, it's revealed that Roen is a devil (technically cerebus), plus Shiki gets the most disrespect of the Student Council, so what better opportunity to assert superiority over a devil dog.