The lack of any observable parallax was considered a fatal flaw in any non-geocentric theory.
From the en.wikipedia.org
The geocentric model was consistent with planetary parallax and was assumed to be the reason why no stellar parallax was observed.
From the en.wikipedia.org
The geocentric model, consistent with planetary parallax, was assumed to be an explanation for the unobservability of the parallel phenomenon, stellar parallax.
From the en.wikipedia.org
The diagram at right shows how daily lunar parallax arises on the geocentric and geostatic planetary model in which the Earth is at the centre of the planetary system and does not rotate.