This is a world where getting good at swords meant being able to parry nuclear level magic bullshit or split a mountain in half. And one of the person who is at tha level in the story is a woman who owns the title of Water Sword God.yeah sure eris is bad at communicating. that's not her problem. her problem is she thinks, and this manga thinks, it could ever be reasonable for her, a woman, to go out (alone) and be an adventurer, as a means to the end of being a more fit partner for him.
that's not what women are.
It is reasonable to think of getting stronger as a way to be equal to the person you're fond of. Especially since she is trying to be a match for Rudeus, the guy who survived and rebounded back after facing against what is considered as a legendary being in the world.
The problem isn't the fact that eris wants to get stronger. It's that she didn't consider telling rudeus about it face to face due to her social ineptitude.