Why were Venus's observed phases the single most powerful proof for the Sun being central?

Answer

A full phase of Venus is impossible to see if it orbits the Earth

In the Ptolemaic system, Venus could only appear as a crescent or new phase. Seeing Venus exhibit a full illuminated face was a direct consequence only explainable if Venus orbited the Sun.

Why were Venus's observed phases the single most powerful proof for the Sun being central?
Galileoastronomyscientistuniverseheliocentrism