Because the sun does not rise.
June is midwinter in the Southern Hemisphere. Antarctica experiences polar night — 24 hours of darkness — from roughly mid-March to mid-September at the South Pole, and for shorter periods at lower latitudes (e.g., ~4 weeks at 66°S, the Antarctic Circle).
The Earth's axial tilt (23.5°) points the South Pole away from the sun during austral winter. Solar elevation remains below 0°; UV radiation is negligible. No sun = no tan (and no vitamin D synthesis).