The modern world treats astrology as a pseudoscience for the reason that its predictions are unreliable, untestable and that it is not based on solid scientific principles. We disagree for the following reasons.
One, astrological knowledge can be built from first solid principles; principles that predate modern science and thus cannot be described within scientific vocabulary, much in the say way that Ayurvedic knowledge cannot be defined or reduced via modern medical principles. One could say that astrological knowledge is built using a different system of variables and principles than science; one can find a detailed description of these principles in ancient texts, begining from Bruhat Hora Parashara written by the ancient sage Parashara. The variables that science is interested in are largely physical and tangible (including say temperature, mass, time, charge, and so on); the variables that astrology is interested in are largely non-physical and intangible. For instance, astrology looks at houses, planetary energies and their distribution in the houses, where the houses signify certain areas of your life. These are all intangible aspects of one's life and cannot be discerned from the lens of modern science.
Additionally, this astrological knowledge is built on the ancient astronomical knowledge in India and elsewhere; many are surprised to learn that Indians, Greeks and many other ancient civilisatons were so adept as astronomy that they could point to and calculate planetary coordinates precisely. Several academic books are published by leading university presses across the world discussing the astronomical achievements of the ancient civilisations. Astrology (Jyotisha) was only a part of this repertoire of knowledge.
Two, modern science treats the world in pieces, where each entity has an independent existence. Ancient wisdom, including astrological wisdom, treats the world as an organic whole where the world is an interdependent entity. If the world is an organic interdependent whole, then our microcosm (our mind and bodies) and the macrocosm (the world outside, including the most visible aspects of it - the planets) are aligned with each other. It is this alignment that an astrolger tries to read with the help of a simple model that contains only nine planets (nine in Vedic astrology, more in western astrology).
Ideally speaking, one should read and interpret the alignment of the entire macrocosm, including every single star and planet around us to read one's destiny the most precisely. But doing so is not within human abilities, at least not so far and therefore we use simple astrological models to decipher this alignment and see what it means for the microcosm or our lives.
One can think of astrological charts/models in the same way as one thinks of highly idealised mathematical models -- they are both idealised and highly simplified description of the world and aim to provide us useful knowledge to navigate the world. Merely because one is true does not make the other one false -- they describe the world at different levels of reality, much in the same way that the truth of biology does not deny the truth of physics or sociology. They can co-exist and it is not necessary that for their co-existence one needs to be able to entirely reduce on branch of knowledge to another. It is an open debate in the scientific and philosophical communities as to whether different branches of science are reducable to one another.
Three, astrological knowledge can well be tested and be relied upon but not in the same way as that of modern science, for the reason that it involves individuals and their will.