Could you treat one as a protagonist and the other as the antagonist, arbitrarily?

Think of it this way. If Person B is Person A's antagonist, then A is B's antagonist in B's personal story. Just because you happen to be telling both stories simultaneously doesn't mean they aren't each other's antagonists.

Another way to look at it: if person A is avoiding a relationship with person B because of a feeling, then person A is their own antagonist.

Either way, I would explore the background of whichever character you didn't profile and background as your protagonist, and discover what it was in their history that made this situation difficult for them.

Cheers,
Michelle