Why do electrons flow from cathode to anode during the flow of electron current?

By definition, a cathode is a negatively charged electrode (a metal plate or a wire), and an anode is a positively charged electrode. An electron is a negatively charged particle. The electrostatic force is attractive when it acts between the two unlike charges (that is, between a positive and a negative charge), and it is repulsive when it acts between the two like charges (between two positive, or between two negative, charges). Therefore, electrons are repelled by the cathode and are attracted to the anode, which results in the current of electrons flowing from the cathode to the anode.

Another way to look at is by considering that there is an electric field `vecE`  in the space between the cathode and anode. Electric field between the two plates with unlike charges is directed away from the positive plate and toward the negative plate. The electric force on a charge placed in an electric field is directed the same way as the field for positive charges, and in the opposite direction  --  for negative charges. Since electrons are negative, the electron force on them is directed opposite the field, or towards the anode. This force makes the electron current flow from the cathode to the anode.