Why isn't aluminium extracted from its ore by a process similar to the blast furnace.?

Because Al is too reactive an element to be freed from its ore using most common processes. You would have to use a more reactive element - Magnesium would do the job nicely (if you could find enough magnesium), but the best way of getting free aluminium is by electrolytic methods. Basically Al is too electropositive to be extracted from its ore using blast furnace type methods...

Because it is more reactive then carbon to be extracted in a blast furnace. Remember carbon is the reducing agent and for it to work the metal being extracted has to be lower in the reactivity series, e.g. iron

Maybe so