Sodium cannot be extracted by the electrolysis of brine solution because

Brine solution is NaCl+H2OElectrolysis: NaCl→Na++Cl- H2O→H++OH-Reduction potential order of cations : H+ > Na+Oxidation potential order of anion : Cl->OH- → Cation which is having high reduction potential is depositing or liberating as gas  at cathodeAt Cathode [Reduction] : H+ + e- → 1/2H2At anode [Oxidation] : Cl-→12Cl2+e-                                 Na++OH-→NaOH→ Anion which is having high oxidation potential is depositing (or) liberating as gas  at anodeIn the extraction of Na metal from brine solution H+ is more easily under reduction at cathode than Na+ ion (or) in another words Na is being move electropositive element than hydrogen, therefore H2 is liberated at cathode and not sodium.