Cicero stated the twins objection (that with close birth times, personal outcomes can be very different), later developed by Saint Augustine. He argued that since the other planets are much more distant from the earth than the moon, they could have only very tiny influence compared to the moon's. He also argued that if astrology explains everything about a person's fate, then it wrongly ignores the visible effect of inherited ability and parenting, changes in health worked by medicine, or the effects of the weather on people.
Plotinus argued that since the fixed stars are much more distant than the planets, it is laughable to imagine the planets' effect on mankind should depend on their position with respect to the zodiac. He also argues that the interpretation of the moon's conjunction with a planet as good when the moon is full, but bad when the moon is waning, is clearly wrong, as from the moon's point of view, half of her surface is always in sunlight; and from the planet's point of view, waning should be better, as then the planet sees some light from the moon, but when the moon is full to us, it is dark, and therefore bad, on the side facing the planet.
Favorinus argued that it was absurd to imagine that stars and planets would affect human bodies in the same way as they affect the tides, and equally absurd that small motions in the heavens cause large changes in people's fates. Sextus Empiricus argued that it was absurd to link human attributes with myths about the signs of the zodiac. Carneades argued that belief in fate denies free will and morality; that people born at different times can all die in the same accident or battle; and that contrary to uniform influences from the stars, tribes and cultures are all different.
These philosophers are all Greco-Roman.
According to Prof Tzvi Langermann's article, one argument used since antiquity was mass disasters. How could a group of people with births of different astrological significance all perish simultaneously? He cites Dom David Amand's Fatalisme et liberté dans l'antiquité grecque p. 53-55. I assume from the title that this is the argument of Greek philosophers.