The reasons against incest are beyond Biblical. Modern science has shown many of the Biblical laws to be sound. If I did not believe in God, I might find it amazing at how these early people could create a set of laws without the scientific knowledge that we have today which would support these laws.
In many countries today, as close as first cousins are allowed to marry. In some countries it is quite common for first cousins to marry, primarily to maintain the wealth within the family. I do not know of any country which allows brothers and sisters to marry.
Research has found evidence that humans actually have a natural aversion to brother-sister incest. It is innate, not learned.
Another problem that arises from incest is that it causes social dysfunction in families. It disrupts the family unit. It can cause emotional and psychological problems.
Incest also increases the risk for undesirable genes to be passed along. These might be genes that cause physical defect, disease, or even psychological disorders. You can see the effects of these in populations where it has been common to marry within a community for many generations. There are certain genetic disorders that are common to Ashkenazi Jews, Amish, etc. Ashkenazi Jews undergo genetic screening and counseling prior to marrying in modern times, because of how frequent certain disorders are passed along. In certain places in Finland where population have intermixed, you find higher than average rates of schizophrenia. Suppose you have a recessive genetic trait for a disease. In a large gene pool with a variety of people, the odds are small that the random individual chosen would also share that same recessive trait. If you narrow the gene pool and marry only within families for several generations, then the odds become extremely high that you will select an individual who carries the recessive trait.
From a Biblical perspective, we do find cases early on in the Bible where incestuous marriages occurred. I believe that these were allowed early on in order to populate the earth-- be fruitful and multiply. Once populated, the door closed. There are a couple of theories that I have heard..... 1) Adam and Eve may have had enough genetic variation within them that their offspring were very much genetically different. 2) After the tower of Babel, when the languages were confused, people spread out across the earth and through adaptation acquired a great variety of genes (i.e. became the various races and peoples, as they grouped together by language and spread out across the earth.) Whichever of the two theories that you want to believe, or any other theory not mentioned, it really doesn't matter. The main point is that back then, even within communities, was a much greater genetic variation then we see today in isolated communities.
In modern science, we know that siblings share approximately 50% of their DNA. Additionally, the actual number of genes that are in the human body is unknown, but it is thought to be somewhere around 30,000. According to a book by Ridley (2003) it would take just 33 genes, each coming in two different varieties (on and off, for example) to make every human in the world unique.
So, in addition to incest being against Biblical laws, there are other negative effects that arise from it. These affects may be genetic, social, and/or psychological.
I will provide some references and links if anyone wants to study more independently. As a side note, I have not read, nor studied through any of the links below. I have read the Ridley book. Everything I wrote comes from prior learning and research. I can not account for what is said in the following links. I only googled a few random links associated with what I was saying. This list is by far NOT comprehensive in nature, nor does it cover all of the topics I discussed.
Chicago Center for Jewish Genetics Disorders - About Jewish Genetic Disorders
Ridley, M. (2003). Nature Via Nurture. Harper Collins Publishers: New York.
Amish disorders:
Genetic Disorders Hit Amish Hard, Centuries Of Intermarriage Make Rare Diseases More Likely - CBS News
Wiley InterScience :: Session Cookies
News in Science - Scientists explain why incest revolts us - 15/02/2007