We know that -ve electrode is called cathode. Then why is Zinc electrode called anode?

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Solution

When we consider electrochemical cells (that is both electrolytic cell and galvanic cell), then anode and cathode are not merely defined as the electrodes which are positively charged and negatively charged respectively. Anode is defined as the electrode where oxidation occurs while cathode is the electrode where reduction occurs. Now in the Daniel cell, following reaction takes place :
Zn (s) + Cu²⁺ (aq) â†’ Zn²⁺(aq) + Cu (s)
This indicates that oxidation is taking place at the Zn electrode. This is why Zn electrode is the anode. So when the following reaction occurs
Zn â†’ Zn²⁺ + 2e^-
then because of the liberated electrons, Zn acquires a negative charge. This is why it is regarded as the anode even though it is negatively charged.

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