Chirality-induced spin selectivity can enable spin generation by nonmagnetic junctions, but its symmetry requirements remain debated. We show that the symmetry of the junction constrains its polarizing behavior: a spin polarizer requires a chiral junction, whereas an achiral junction can act as a spin filter. This symmetry involves the junction as a whole, not only the molecule. Achiral molecules can act as polarizers or filters depending on junction geometry, as confirmed with a minimal tight-binding model. Reciprocity forbids polarization detection by linear two-terminal magnetoresistance; we propose a nonlocal measurement that distinguishes polarizers from filters and establishes whether the junction breaks time-reversal symmetry.