Many students are taught through grade school and into high school that the anode is positive and the cathode is negative. I was too. Imagine my surprise when I learned that isn't always true. The answer to your question is in the definition. The definition is NOT about the polarity of the electrodes. The definition: Oxidation occurs at the anode. Oxidation is the loss of electrons. So in galvanic cells, the negative electrode is the anode. In electrolysis cells, the anode is the positive electrode.
