Howard F. answered 04/08/21
DMA in Theory/Comp with 20+ Years of Teaching Harmony + Counterpoint.
Perhaps the most important reason it sounds unstable is because the tonic chord is actually a diminished triad. It's the ONLY one of the "white key" church modes that has that structure. If you think about it, locrian mode starting on B is spelled B-C-D-E-F-G-A-B. Using only the notes that are part of that mode, and building a triad from degrees 1, 3, 5 results in B-D-F which is a B-diminished triad.
Our western ears are attuned to wanting such a diminished triad to resolve to a major or minor triad, and to hearing it tend to resolve, in this instance to a C-major or C-minor triad - e.g. C-E-G or C-Eb-G (I in C-major; i in C-minor), or else, perhaps to an A-minor triad A-C-E (i in a-minor), because we tend to hear diminished triads has having either a leading tone - viio (major or minor key) or supertonic - iio (minor key only) function.