There are two different kinds of twins... fraternal and identical. Studies done of identical twins separated at birth and raised by different families show that the identical twins are much more likely to be the same orientation as one another (gay) than individual siblings born of the same mother who were raised by two different families.
This makes sense because identical twins are born of the same egg and sperm. If the egg hadn't split into two entities then only one child would have been born. On the other hand fraternal twins are born of two different eggs and two different sperm. They just happen to be in the womb at the same time.
So the studies findings demonstrate that the majority of "gayness" is biologically based. Similar studies done about things such as breast cancer show the same thing... That identical twins raised by different families tend to both have breast cancer more often than non-identical siblings who are separated at birth. We all seem to accept breast cancer's biological basis, even though not 100% of identical twin females develop it. We've even identified the gene responsible for most hereditary breast cancers. But not everyone with the gene gets it even if they're identical because other biological factors can act on the body in such a way that the gene does not express itself.
All of what I just said is a very simple way of reviewing the research. If you'd like more in-depth answers please go ahead and do some research on your own about genetics and heredity. Not about homosexuality at first, but about other things such as breast cancer or whatever. This way it's about a topic that you don't feel so strongly about so you can have an unbiased mind when reading. Then take that knowledge and apply it to homosexuality and you will see that the similarities between the research on identical twins and other genetic stuff is very similar to the findings of studies on identical twins and homosexuality.
Edit in response to additional comments.
I am a professional in the mental health field. I have just as many qualifications as the people on that narth website that you mention. Most of the diagnoses that were ever in the DSM were blamed on parental relationships or lack thereof at first. Can you believe that the mental health field originally thought autism was brought about by "refrigerator mothers?" Sounds silly now, since we've done more research on it, doesn't it? The mental health field is a social science. As a science it is constantly evolving to take into account new information. Although the mental health field once thought that homosexuality was a mental illness brought on by inadequate family relatinships this is no longer the consensus. This is because we've done more research. I again encourage you to read twin studies on this. You will notice that there is a strong genetic link when it comes to homosexuality. But just like with other things that are genetically based, such as cancer, learning disabilities, and the like, it is not always expressed in siblings due to individual differences that determine whether the gene is expressed or not.
If you had done the research on your own you would have already known that there is no 100% correlation for any complex trait that is genetic. There are high correlations, but nothing that is 100%. If you had done the research you would have known about statistical significance and you would have realized that the results of the twin studies are statistically significant, meaning that the outcome of the study could not be explained by chance.
When I mean doing the research, I mean going to an academic library or paying to be a user of an online academic library and actually doing a literature review. I do not mean picking up the latest issue of Times magazine. It is obvious by the way you worded your question and your additional responses that you have never done a literature review in your life. You depend on articles in popular media and other people's interpretation of the research. Again, go do your own research and become informed through the original studies before trying this question again.