A galvanic cell works basically in reverse to an electrolytic cell.
The anode is the electrode where oxidation (loss of electrons) takes place; in a galvanic cell, it is the negative electrode, as when oxidation occurs, electrons are left behind on the electrode.
The anode is also the electrode where metal atoms give up their electrons to the metal and go into solution.
The electrons left behind on it render it effectively negative and the electron flow goes from it through the wire to the cathode
Oxidation is loss of electrons and it could be possible if it occurs at anode as anode is the electrode which is +vely charged and so it must have lost electrons and so it is the site of oxidation.
The reduction is gain of electrons and it occurs at cathode because cathode as it is negatively charged so it must have gained electrons has the tendency to provide or loose electrons.