Question

How did Venus' phases support Copernicus and refuted Ptolemy?

Answer 1

Actually it was the " full set of phases".

Explanation:

A full set of phases, like our moon, can only be had if the object we're talking about, can get between the light source (=Sun) and ourselves.
Planets farther away from the Sun than Earth have some sort of phases too, but they're always partly illuminated.

You can clearly demonstrate this (to yourself) with a small light source and a couple of tennis (or other) balls.
Or you can go read this:
https://en.wikipedia.org/wiki/Phases_of_Venus
and:
https://en.wikipedia.org/wiki/Planetary_phase