Someone's getting their pronouns confused lol...if she's referring to the MC as nii-san (older brother) then the MC cannot refer to her as nee-san (older sister).
edit: alright I actually read the first panel and got the story but closeness isn't usually associated with the -san honorific as that's typically used by people who respect another person and doesn't show off the closeness (you'd want -chan in that case)