Your astrological chart is unique to you - an astrological chart will not be exactly duplicated for 25,000 years - considered to be a "cosmic year". Yes, even with the procession of the equinoxes, (which should have altered the dates of sun signs somewhat) ... Astrology works.
So the short answer is "I don't know" why ...Nevertheless: Astrology works.
Having calculated charts since the age of nine, I have observed the accuracy of astrology first hand for most of my life. My Grandmother could shake a person's hand and immediately know their Sun sign - She was nearly always correct.
Being that my own Sun sign is in Virgo, I have a rather analytical side to my nature; I love science. Therefore the "whys" of astrology used to bother me a great deal.
From a metaphysical perspective the principle of astrology is not difficult to comprehend - "as above, so below." Understanding the oneness of all things allows us to accept that celestial events are reflected over and over again - from the cosmic to the quantum level.
Astrology has been used by virtually every advanced civilization for thousands of years. It vastly pre-dates most currently popular belief systems. In a sense, it can be thought of as the psychology of the ancient world.
It can also be thought of as a bit of a handbook for your current lifetime.
Being ancient of course, does not make something correct, but note that this study arose from observation about human nature and the correlation with cosmic events - not an arbitrarily assigned belief dependent upon a specific deity.
Records indicate that the ancient Egyptians made use of Astrological observation and data. The Egyptians were very good at making stellar (but not necessarily planetary) observations and also to use these for aligning special buildings and temples. They learned this planetary astrology originally from the Babylonians.
Alexandria, Egypt, was quite possibly the birthplace of "modern" astrology. It was the Persian people who eventually passed on to the western civilizations astrology as we moderns know it, as they had learned it from the Egyptians. Of course, there are other equally interesting forms of Astrology: Chinese and Vedic are just two of these.
I believe that the reason for Astrology's longevity is its value as a tool in the quest for self understanding.
Did you know that your individual birth chart will not be repeated for nearly 25,000 years? This is the amount of time that will pass before all the planets to align exactly as they did at the moment of your birth.
Astrology works in a very holistic and complex manner, and our perception of cosmic events is still very limited. Our perspective of cosmic realities as observed from one tiny fragment of time and space is obviously only partial. Many astrologers also believe that astrology does not work by cause-and-effect influences but rather by a non-mechanical means. Some astrologers would also argue that astrology's purpose is to reveal meaning and significance to our lives, not simply to describe phenomena.
A living being is more than a compilation of mechanical processes, and astrology can aid the personal evolution of an individual.
From this perspective, whether astrology can be validated scientifically is irrelevant. It could be said that astrology is more a language rather than as a science.
Which brings me full circle to my short answer: astrology does "work" -- as an accurate tool for self awareness, relationships, and personal growth. Once you've experienced it, you'll know that much to be true.