Why did greeks reject the orbit sun?

It ran contrary to their senses.
If the Earth rotated, then there should be a "great wind" as we moved through the air.
Greeks knew that we should see stellar parallax if we orbited the Sun - but they could not detect it.

• Apparent shift of a star's position due to the Earth's orbiting of the Sun
• The nearest stars are much farther away than the Greeks thought.
• So the parallax angles of the star are so small, that you need a telescope to observe them

1. Stars are so far away that stellar parallax is too small for naked eye to notice
2. Earth does not orbit Sun; it is the centre of the Universe

Unfortunately, with notable exceptions like Aristarchus, the Greeks did not think the stars could be that far away, and therefore rejected the correct explanation (1)…

Thus setting the stage for the long, historical showdown between Earth-centered and Sun-centered systems.