You should read the essay "Science: Conjectures and Refutations" by Karl Popper. In short, although astrology may use things like observation, it is not scientific. Why? Well you answered your own question, it's made up of extremely vague statements that will always be true. The virtue of a scientific theory is not in its ability to be proven true, but its ability to be proven untrue.
Let me use a simple analogy:
Let's say I tell you that I have a theory about why people commit murder. I say the sole reason why people are killers is because they had poor relationships with their parents, or if they were orphans with the major adult figures in their lives.
Now, say we look at some samplings of convicted murderers, there are no cases where you can not interpret their childhood as satisfying my criteria above.
I'm anticipating some disagreement with what I've said, so let me find some random examples and I'll try to show how each can be interpreted to agree with my hypothesis no matter the case.
First one "Luis Alfredo Garavito Cubillos": Here is a short blurb about him,
"Garavito's victims were poor children, peasant children, or street children, between the ages of 8 and 16. Garavito approached them on the street or countryside and offered them gifts or small amounts of money. After gaining their trust, he took the children for a walk and when they got tired, he would take advantage of them. He then raped them, cut their throats, and usually dismembered their corpses. Most corpses showed signs of torture."
This fits my original hypothesis because the victims were all children. Clearly he had a poor childhood as a result of the upbringing his parents gave him, which resulted in his neuroses and violent thoughts towards children. The fact that he gave them gifts also shows that his parents most likely had a poor relationship with him, and he is expressing negative behavior towards typical parent-child actions such as giving a child candy or gifts.
Let's look at another one.
"Daniel Camargo Barbosa" : According to wikipedia "Camargo's mother died when he was a little boy and his father was overbearing and emotionally distant. He was raised by an abusive stepmother, who punished him and sometimes dressed him in girls clothing, making him a victim of ridicule in front of his peers"
This obviously fits the hypothesis as well, his mother was abusive, so it fits the hypothesis. We're doing pretty good with this idea right?
And another one: "Ahmad Suradji"
"He told police that he had a dream in 1988 in which his father's ghost told him to kill 70 women and drink their saliva, so that he could become a mystic healer"
The reason why he committed his crimes is because of his relationship with his father, which is evident by the "ghost of his father" telling him to kill the women.
And yet another one: "John Wayne Gacy"
"Throughout his childhood, Gacy strove to make his father proud of him, but seldom received his approval: One of Gacy's earliest childhood memories was of being beaten with a leather belt by his father at the age of 4"
This also fits my hypothesis, he had a poor relationship which lead to him becoming a killer.
That's enough, I think my point has been made. In any situation the evidence could be interpreted as confirming the original hypothesis even if there was no clear evidence that it was their relationship that caused them to become serial killers
If my original hypothesis had been more specific, such as "all people who have poor relationships with their parents or parental figures will become killers" then it would be much easier to disprove, and thus a much more useful hypothesis.
One of the things that most believers in astrology will do when presented with refuting evidence is to use interpret the evidence in such a way that it either does not refute astrology or confirms it. If you look at any scientific theory you will see that it's possible for it to be wrong if there is evidence that refutes it, and in fact there are many cases where scientific theories have been proven wrong by observations made after formulating the hypothesis.
The key idea to show why astrology doesn't work in my opinion is its lack of riskiness, you may feel that the statements are very accurate, but this is only due to the fact that they are meant to be overly generic.
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You should read the essay "Science: Conjectures and Refutations" by Karl Popper. In short, although astrology may use things like observation, it is not scientific. Why? Well you answered your own question, it's made up of extremely vague statements that will always be true. The virtue of a scientific theory is not in its ability to be proven true, but its ability to be proven untrue.
Let me use a simple analogy:
Let's say I tell you that I have a theory about why people commit murder. I say the sole reason why people are killers is because they had poor relationships with their parents, or if they were orphans with the major adult figures in their lives.
Now, say we look at some samplings of convicted murderers, there are no cases where you can not interpret their childhood as satisfying my criteria above.
I'm anticipating some disagreement with what I've said, so let me find some random examples and I'll try to show how each can be interpreted to agree with my hypothesis no matter the case.
I'm simply going to go through a few of the people on this list: http://en.wikipedia.org/wiki/List_of_serial_killers_by_number_of_victims
First one "Luis Alfredo Garavito Cubillos": Here is a short blurb about him,
"Garavito's victims were poor children, peasant children, or street children, between the ages of 8 and 16. Garavito approached them on the street or countryside and offered them gifts or small amounts of money. After gaining their trust, he took the children for a walk and when they got tired, he would take advantage of them. He then raped them, cut their throats, and usually dismembered their corpses. Most corpses showed signs of torture."
This fits my original hypothesis because the victims were all children. Clearly he had a poor childhood as a result of the upbringing his parents gave him, which resulted in his neuroses and violent thoughts towards children. The fact that he gave them gifts also shows that his parents most likely had a poor relationship with him, and he is expressing negative behavior towards typical parent-child actions such as giving a child candy or gifts.
Let's look at another one.
"Daniel Camargo Barbosa" : According to wikipedia "Camargo's mother died when he was a little boy and his father was overbearing and emotionally distant. He was raised by an abusive stepmother, who punished him and sometimes dressed him in girls clothing, making him a victim of ridicule in front of his peers"
This obviously fits the hypothesis as well, his mother was abusive, so it fits the hypothesis. We're doing pretty good with this idea right?
And another one: "Ahmad Suradji"
"He told police that he had a dream in 1988 in which his father's ghost told him to kill 70 women and drink their saliva, so that he could become a mystic healer"
The reason why he committed his crimes is because of his relationship with his father, which is evident by the "ghost of his father" telling him to kill the women.
And yet another one: "John Wayne Gacy"
"Throughout his childhood, Gacy strove to make his father proud of him, but seldom received his approval: One of Gacy's earliest childhood memories was of being beaten with a leather belt by his father at the age of 4"
This also fits my hypothesis, he had a poor relationship which lead to him becoming a killer.
That's enough, I think my point has been made. In any situation the evidence could be interpreted as confirming the original hypothesis even if there was no clear evidence that it was their relationship that caused them to become serial killers
This is what's known as post hoc ergo propter hoc reasoning: http://en.wikipedia.org/wiki/Post_hoc_ergo_propter_hoc and it also falls under confirmation bias: http://en.wikipedia.org/wiki/Confirmation_bias
If my original hypothesis had been more specific, such as "all people who have poor relationships with their parents or parental figures will become killers" then it would be much easier to disprove, and thus a much more useful hypothesis.
One of the things that most believers in astrology will do when presented with refuting evidence is to use interpret the evidence in such a way that it either does not refute astrology or confirms it. If you look at any scientific theory you will see that it's possible for it to be wrong if there is evidence that refutes it, and in fact there are many cases where scientific theories have been proven wrong by observations made after formulating the hypothesis.
The key idea to show why astrology doesn't work in my opinion is its lack of riskiness, you may feel that the statements are very accurate, but this is only due to the fact that they are meant to be overly generic.