I'm afraid the law of biogenesis (which came from science) does say that life cannot come from non-living mater. I'm sorry, but that is scientific. You may mean that there is nothing in science that makes any law of science absolute. If that's what you meant, then maybe I'll agree with you. However, the law does exist, and it does stand until further observations refute it.
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Law of biogenesis is not a law born out of theoretical predictions as well as observations; it is supported only by observations of the modern world, and as such, can only be called a theory. So, don't try and base your arguments off of the premise that what you are arguing is law. What you are saying is a simple matter of confounded logic, as many on this thread have pointed out.
You mean to say that all life comes from preexisting life, and that we couldn't have come about from nonliving materials. A fascinating theory. But think about an analogous case. Let's talk about evolution. Suppose that a person in malaria ridden Africa breaks out with sickle cell anemia due to a point mutation in his genes that causes a mistake in the structure of the hemoglobin in his blood. Of course, this person is now immune to malaria, and his mutation is selected for and is passed on to his descendants. Soon enough, the entire population has the gene for sickle cell anemia, and are, for the most part, all immune to malaria. Disregarding the obvious side effects of SCA, this mutation is beneficial and is a microevolutionary step. A hundred years in the future, the only people that remain are those with the SCA gene, and some man, perhaps a descendant of yourself, posits that his population must have always had the SCA gene, and couldn't possibly have gotten it from some unnatural way.
After all, all modern observations support the man's theory. No new sickle cell genes come about, and only previous genes in previous generations beget new genes in younger generations.
But in the end, the man is wrong. There was a time when his people didn't have the gene. The gene came about in a mutation in the normal hemoglobin protein.
This is akin to the situation you find yourself in. How can you say that 3.8 billion years ago, the first life didn't evolve from nonliving materials? You can't. You cannot call the law of biogenesis a law. It is only a theory. And yes, it is taught in schools in the form of Pasteur's experiments and the like.