why can't you use Carbon to extract Aluminium?

Question

and
How do you extract Aluminium using elecrolysis?

Answer 1

http://www.chemguide.co.uk/inorganic/extraction/aluminium.html

Answer 2

Aluminium is too reactive and might form stable compunds.
Aluminium is first extracted from its ore(bauxite) after being purified by NaOH. This is then mixed with cryolite(Na3AlF5) wich lowers its melting point to about 900 degrees Celcius. This molten mixture is then electrolysed. Molten Al will collect at the cathode and O2 gas is given off at the anode.