Let's start with a quick disclaimer. We aren't researching the causes of divergent sexualities to "cure" them. We're researching them because it's cool and interesting. If you're here to collect information for your weird eugenics-y viewpoints I kindly invite you to fuck right off. With that out of the way, let's get sciencing.
We've known for a long time that there's... some kind of hereditary component to homosexuality (Pillard and Baily, 1998). By the turn of the century, there had already been plenty of studies that found that homosexuality was more common in certain families. It's also pretty generally accepted that non-heterosexual men are far more likely to have non-heterosexual brothers than what would be expected by random chance alone (Pillard and Weinrich, 1986), and that identical twins (two individuals with the same genome) are more likely to have similar sexualities than fraternal twins (two individuals with distinct genomes) (Bailey and Pillard, 1991). What's more, these trends still exist, albiet less intensely, even when siblings were raised by different families (Bailey et al, 1993). All this together leads to the general consensus that both a person's genetics and the environment that they're raised in play a role in shaping their sexuality.
A lot has changed in genetics in the last 20 years, though. So perhaps you might be thinking that DNA sequencing has put this question to bed already. Unfortunately, you'd be wrong. One of the best tools for identifying the genetic basis of a trait is something called a GWAS, or a genome wide association study. Basically, you scan the genomes of people with a trait and without a trait. Then, you search for any mutations or genetic variations that are found in the people who have that trait, but not found in people who don't have the trait. What you get in the end is a list of genetic signatures that only or preferentially occur in individuals with the trait. A lot of the time, those signatures create the trait, or at the very least, are related to it.
A GWAS works pretty well when the trait you're looking at is non-complex. That is, a trait that is strongly controlled by a small number of genetic signatures. However, we already know that human sexuality is pretty complicated. We also know that it isn't even entirely genetic! GWAS studies of these kinds of characteristics run into trouble because of something called statistical power. Basically, with a simple genetic trait that's turned on and off by one mutation, it's pretty easily to tell which mutation is causing the trait. Everyone with the trait has that mutation, and everyone without the trait does not have the mutation. Pretty cut and dry, right? Well, as traits get more complicated -- controlled by more and more different genes and more and more different non-genetic factors -- it becomes more and more likely that some genetic alterations associated with homosexuality will be found in non-homosexual individuals, and vice versa. When you look at a small number of people, the resulting data can be confusing and unclear. So, the more complicated a trait is, the more genomes you need to look at for your data to make any sense at all.
