What is the real reason for evaporative cooling?

Which is the correct explanation?

This is not an either-or question. Both explanations are correct. The first explanation is from a microscopic perspective while the second explanation is from a macroscopic perspective.

because liquid molecules need to absorb latent heat to change from the liquid state to the gaseous state, increasing their potential energies rather than their kinetic energies, evaporative cooling occurs because this energy is absorbed from the bulk of the liquid itself, and therefore decreases the average kinetic energy of the remaining liquid particles.

"Molecules need to absorb latent heat" is just meaningless word salad.

How about if we formulate it like this:

Because only a liquid molecule that has stolen kinetic energy from other molecules can escape the other molecules, cooling of remaining molecules occurs when some molecules escape.

And those escaping molecules use up the stolen kinetic energy in the escaping process. The kinetic energy of the escaping molecules decreases while the potential energy of the escaping molecules increases.

Both explanations are correct, but I believe the first explanation is more focused on the specific phenomenon of evaporation, though I have some issues with the wording of the first sentence.

Evaporation differs from vaporization in that it occurs strictly at the surface of the liquid and at temperatures below the boiling point of the liquid. For example, an open glass of water will evaporate at room temperature. Vaporization occurs within the liquid and at the boiling point of the liquid.

Regarding the first description, it is true that as heat is transferred to a liquid the average kinetic energy of the molecules increases, i.e., the temperature of the liquid increases. But you don’t have to increase the temperature of the liquid for evaporation to occur. Increasing the temperature of the liquid increases the rate of evaporation, but is not required for evaporation to occur.

Evaporation occurs because not all molecules have kinetic energy equal to the average. They are distributed around the average. The molecules within the liquid having higher kinetic energy than the average remain within the liquid. The molecules having higher kinetic energy at the surface of the liquid are able to escape into the air, as long as the kinetic energy is great enough to overcome surface tension and intermolecular forces at the surface. When the higher kinetic energy molecules escape it results in lowering the average kinetic energy of the remaining molecules at the surface. So there is localized cooling of the liquid at the surface (a.k.a. evaporative cooling) below the bulk temperature within the liquid. This results in heat transfer from within the liquid to the surface of the liquid in order for evaporation to continue, as discussed in the second explanation. Essentially, there is a transfer of kinetic energy from within the liquid to the surface of the liquid.

Regardless of whether it is evaporation or vaporization, energy is required to convert the liquid to a vapor. That energy is called the latent heat of vaporization.

Hope this helps.