@Garlyle
She only started figuring out that she likely was the Saint recently. She pieced together her own high level, the fact that the other girl had a low level, and her own proficiency in Holy magic and started coming to the realization. Even if her own status indicated she was the Saint, there was no reason to believe the other girl summoned was not also a Saint especially when you consider that no one came to her to actually test her abilities.
Then consider that she's been summoned to this world against her will, for the sole purpose of being burdened with the responsibility to become their holy maiden. Consider also that the summoning brought in an extra girl and that after being judged on their beauty, she was the one discarded and ignored. She had little reason to feel grateful and to want to help.
There's also every reason to believe that the other girl would be protected well if she was considered the Saint and she also knew that if she revealed that she was the Saint then the other girl would lose her status; she'd be the worthless extra summoned by mistake, having lost her life in her previous world for no good reason at all.
She doesn't lack conviction, she is simply a complex character who is actually considering the situation and trying to figure out what she should do. It's only natural to be conflicted.
