Which way to draw diode in a circuit diagram
In normal circuit analysis, we almost never think about which way the electrons are flowing. We nearly always calculate and visualize how the "conventional current" is flowing.

In the case of a diode (to simplify things somewhat---see Steven's answer for some special cases), conventional current flows through the diode from the anode to the cathode; that is, conventional current flows in the direction that the "arrow" of the diode symbol is pointing.