Why is the electrode potential for a cathode positive?

The question: Why is the electrode potential for a cathode positive?

Since question didn't directed to what kind of cell, the answer is it is not always positive:

As M. Farooq clarified, cathode is where reduction is happening in a cell. Thus, in Galvanic cell it is positive as the reduction reaction, $ce{Y+ + e- -> Y}$, happens. The electrons needed for this purpose came from the anode. However, in an electrolytic cell, electrons from an outer source (e.g., a battery), flow to the negative end where the reduction reaction, $ce{M+ + e- -> M}$, happens. Thus, the cathode is negative here.

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Edit: I agree with Poutnik's comment below. Accordingly, it may be better to say cathodes are more negative than anodes in electrolytic cells and more positive than anodes in galvanic cells. As more positive does not mean positive and more negative does not mean negative. The convention of marking positive and negative cell contacts is good enough for every day life, but it says nothing about the sign of electrode potentials either with respect to free electron or SHE (e.g., relevant half-cell reduction reaction's potential may carry positive or negative sign, based on the corresponding reaction).

I think your source of confusion is the name cathode and anode. Anode and cathodes have nothing to do with the electrostatic sign. They have to do with the processes.

Cathode, whether electrostatically positive OR negative, is the electrode where reduction is occurring.

Anode, whether electrostatically positive OR negative, is the electrode where oxidation is occurring.

Hope that clarifies your confusion about the signs.

Electrode potential is the potential difference between the electrode and the surrounding electrolyte.

This is not the electrode potential but is rather called interfacial potential difference.

Mathew wanted to elaborate this further on "Electrode potential is NOT the potential difference between the electrode and the surrounding electrolyte". I think this an electrochemist's unfulfilled dream to find the absolute potential difference, i.e., we dip Cu electrode in a copper solution and we measure the potential difference between the two. I think one can improvise what Poutnik is saying. The tabulated electrode potentials, found commonly, are not the potential differences of metals and their solutions. The reason is that it is impossible to measure such a hypothetical construct.

Electrode potential is NOT the potential difference between the electrode and the surrounding electrolyte.

The electrode potential is conventionally the relative potential to the reference standard hydrogen electrode(SHE) with conventionally assigned potential 0 V.

The "absolute" potential of the SHE wrt a free electron potential is then estimated as $pu{+4.44 pm 0.02 V}$.

Cathodes are more negative than anodes in electrolytic cells and more positive than anodes in galvanic cells. But more positive does not mean positive and more negative does not mean negative. The convention of marking positive and negative cell contacts is good enough for every day life, but it says nothing about the sign of electrode potentials ( either wrt a free electron in vacuum either wrt SHE ).

The electrode potentials can be positive + negative, or both positive or both negative wrt SHE. They are always positive wrt a free electron.