How can you know it's not a coincidence?
There are too many reasons why your experiences are difficult to evaluate. Selection bias, for a start. The amount of premonitions I have had of my parents', or family's death in general is exactly as many as the amount of false premonitions. So if anyone else gets a premonition and it turns out to be right -- why is your experience psychic and not coincidental? How many false readings do you have? Possibly any you do have you discount or forget about, leading to a perception that you are highly successful in being psychic, but on a cold hard examination it's just more likely to be luck really.
So far the Scientific method has managed to explain a phenomenal amount about the way our world works. It has also barely scratched the surface in some ways. There are a number of principles, though, that suggest that psychic abilities ought not be possible:
1. There is no particular reason why you should have them and I do not. The "I just have a closed mind" line doesn't really work for me, as I am not usually in control of my mind.
2. Often psychic abilities imply communication between two points a long distance apart -- this violates causality and the assumption that causality holds has never yet been shown to be wrong.
3. There is no particular reason either, why psychic abilities never manifest themselves when we are testing them. The James Randi Challenge requires that people claiming to be psychic agree to conditions of a test of their abilities beforehand. To date, no test has been successful (
http://en.wikipedia.org/wiki/One_Million_Dollar_Paranormal_Challenge ) even though before the experiments claimed psychics were happy with the conditions.