How could any reasonable thinking human being believe in Astrology?  Let me tell you how.

First let us begin with what astrology is not.  Astrology is not the horoscope books that you pick up up at the grocery store by the check lines.  No reasonable person could believe in those, indeed.  Medieval and Renaissance astrology was based on a model of the universe that differs significantly from our own.

Let us begin with the proof: How can the planets in their celestial orbit influence life on Earth?  Early astrologers had plenty of reason to believe that they did.  Let us go over a few fairly self-evident proofs that would have established strong evidence at the time.

1) The Moon and Sun Affect the Tides.

In the absence of Newton's Law of Universal Gravitation and the general Theory of Gravity Medieval and Renaissance sailors were left attempting to describe a mechanism of influence based only on observation.  Although they did not have access to these more modern scientific ideas, they were still clever mathematicians and were able to fairly precisely model the relationship between the positions of the Sun and Moon in the sky and the tides.  They had solid proof of influence and were left with a model lacking a mechanism.

2) The Moon and Sun emit light.

In the absence of the Cartesian Theory of light, Newton's Corpuscular (or particle) theory of light, and modern wave-particle duality as explanations for the phenomenon Medieval and Renaissance Astrologers were left only with the clear observation that the Sun and Moon in the sky were able to produce the same effect of illumination that fire did, but did so eternally and without consuming fuel.  This implied that the emission of light was an innate quality of these two bodies, as well as all other planets and stars.  Certainly modern astrology critics will not disagree that distant stars affect us by shedding light upon us from across the galaxy.

3) When the Sun is in Scorpio Pumpkins, yams, and other gourds ripen.

Every year at harvest time, the Sun is in Scorpio.  This occurs in late October and early November.  This is coincedence in its purest form, as these two events always coincided with perfect reliability.  A farmer could look to the night sky just as easily as he could look to the seasons to determine how far away the harvest was.  When seen in light of of the previous two examples there was a strong and, actually, quite compelling reason to believe that this relationship was causal.

4) Elemental Sphere Theory.

As a response to these, and countless other seasonal, monthly, or daily events that coincided with specific astrological events, Classical, Medieval, and Renaissance scholars developed a working model of the universe.  According to their model the universe was composed of five spheres.  The first four spheres were the elemental spheres.  In order from lowest to highest they were: The sphere of Earth, the Sphere of Water, the Sphere of Air, and the Sphere of Fire.  The fifth Sphere was the Aether, which composed the planets and stars.

These elements were in this order for a specific reason.  Each sphere naturally flowed to its position in the hierarchy like differently weighted liquids in a glass.  As such Earth sinks the lowest and is the heaviest.  Next is water, which also falls downward unless there is earth below it.  The third, Air, will rise from beneath water to its rightful position above these first two.  the last, fire, will attempt to rise in all circumstance.  Left to their own devices, over time, there elements would return to their natural states as a series of perfectly concentric spheres.  This is, in a sense, an early precursor to the idea of entropy.

As a model for the observable world this theory served mankind quite well.  It provided a causal explanation for observed phenomena and even accurately predicted the behavior of other materials.  This explains the process of erosion, by which rigid structures composed of Earth will, over time, smooth, flatten, crumble and return to their natural place below the the spheres of air and water.  it also explains precipitation and the flow of water downhill, as the matter descending from the sphere of water will naturally return to the lowest point it can so that it will rest below air.  it even explains why thin balloon-like objects (paper zeppelin toys, in this example) rise when held over a flame, as the trapped essence of fire carries them above the sphere of air.

5) Missing links.

With so much seeming evidence stacked in their favor, astrologers began looking for the causal relationships between other celestial bodies and the world below.  It is in this arena that the more dubious claims of astrology were made.  As Astrologers theorized that, if humans were composed of the elements as well, then the planets should affect them just as the affect the temperature, season, or tides.  Thus was born the personal horoscope.  there is no good reason why, given their model of reality, this would nto be true.  The astrologers who practiced this enjoyed a short popularity, but the unreliability of their predictions was well known even in the Middle Ages.  Serious astrologers did not respect them, and it is from the divide that the difference between modern "astronomy" and "astrology" is born.

Modern contempt for medieval astrology is little more than anachronism.  We hold against men living in the 1100's the ignorance of Copernicus' Heliocentric Model of the Universe (which has itself been superseded, as we no longer believe that the Sun is the center of the universe either).  We blame them for the lack of understanding of atomic theory, the wave-particle duality of light, and myriad other scientific discoveries.  This is especially ironic because, in the absence of these theories it is these very philosophers, astrologists, astronomers, and mathematicians who worked, studied, experimented, and ultimately invented these very ideas that would shape modern science and rationalism.

To fall for the little horoscope book at the check-lane, however, is to be duped by millennia-old pseudo-science with no foundation in observational evidence, leaving you little better than the czars of Russia, enchanted by Rasputin as they fell from power, or the petty kings of France who squandered their patronage on Nostradamus.  Astrology was only ever intended to predict the seasonal, and explain the mechanisms of the natural world in the best terms available at the time.