In The Republic of Plato, there's this idea of rotation between political regimes[0], and it's explained by the way each generation treats the next one. Down to Earth example: think of overprotecting parents making their child unprepared for an ordinary adult life.
Now of course, this is again distant from the discourse of our favorite astrologers, but if you squint a little, there are conceptual similarities.
Thinking about it a little more, and on point to your original remark, I wonder if the fact that a considerable amount of people like to believe in astrology isn't tied to the same instinct that made old people personify everything and anything as Gods: a strong tendency to see order and intelligence in chaos.
After all, science is still about doing just this, minus the anthropomorphism. So, not so shocking: just human nature at works.
[0]: https://en.wikipedia.org/wiki/Republic_(Plato)#Book_VIII%E2%...