*You* disprove that homosexuality is nature's design of or for birth control.

" is randomly generated with 'designs' being patterns that began as random mutations and didn't get naturally selected out. "

What does" generated " mean as you say?

A form or stage in the life cycle of an organism.

All of the offspring that are at the same stage of descent from a common ancestor.

The average interval of time between the birth of parents and the birth of their offspring.

A group of individuals born and living about the same time.

A group of generally contemporaneous individuals regarded as having common cultural or social characteristics and attitudes.

The act or process of generating; origination, production, or procreation.

Definition of generate

transitive verb

1: to bring into existence

b: to originate by a vital, chemical, or physical process 

You say you deny something being designed but has a design.

This is like tomato tomah-to. Something that has a design has a structure. A design is a structure. 

It's something that has a particular form, shape, make.

design
 noun

Definition of design (Entry 2 of 2)

1a: a particular purpose or intention held in view by an individual or group

b: deliberate purposive planning

2: a mental project or scheme in which means to an end are laid down

3: a deliberate undercover project or scheme 

5a: an underlying scheme that governs functioning, developing, or unfolding : PATTERN, MOTIFthe general design of the epic

b: a plan or protocol for carrying out or accomplishing something (such as a scientific experiment)also : the process of preparing this

That in itself is separate from what brought it about in regards to whether there was premeditation or intent or arbitration.

Just like you can say all of the solar system is a design from the big bang if one believes that.

Also anything that is innate and not externally influenced by education or programming is natural.

In other words,  something that just is alone.

"Being gay was simply a trait that didn't get selected out"

Selected out naturally or was it done socially?

"There was not enough reason for homosexuality to get selected out, there was absolutely no design involved."

Let's break this down.

What is homosexuality?

It's the desire or desire and act of acting on those desires of sexual activity with the same sex based on being attracted to do so.

• You don’t have to be dating or have a sexual experience with someone to know you’re straight, gay, lesbian, bisexual or queer. You might be doing these things and still not feel sure about your sexuality.
  

Can other people tell what my sexual orientation is?

No. A person only knows your sexual orientation if you tell them. Sexual orientation describes how you feel inside, and only you know what it’s like to be you.  

Some people may think they can guess if a person is lesbian, gay, or bisexual based on superficial factors like how they look, dress, or behave. These are stereotypes, or very simplified judgments, about how lesbian, gay, and bisexual people act. But just like heterosexuals, there are many different ways that homosexual and bisexual people look, dress, and behave. Using stereotypes to label someone else’s sexual orientation can be inaccurate and hurtful.

Now where does this derive from ?

You mentioned about mutations. Well mutations of what?

Chromosome linkage studies of sexual orientation have indicated the presence of multiple contributing genetic factors throughout the genome. In 1993, Dean Hamer and colleagues published findings from a linkage analysis of a sample of 76 gay brothers and their families.[34] Hamer et al. found that the gay men had more gay male uncles and cousins on the maternal side of the family than on the paternal side. Gay brothers who showed this maternal pedigree were then tested for X chromosome linkage, using twenty-two markers on the X chromosome to test for similar alleles. In another finding, thirty-three of the forty sibling pairs tested were found to have similar alleles in the distal region of Xq28, which was significantly higher than the expected rates of 50% for fraternal brothers. This was popularly dubbed the "gay gene" in the media, causing significant controversy. In 1998, Sanders et al.[citation needed] reported on their similar study, in which they found that 13% of uncles of gay brothers on the maternal side were homosexual, compared with 6% on the paternal side.[35]

A later analysis by Hu et al. replicated and refined the earlier findings. This study revealed that 67% of gay brothers in a new saturated sample shared a marker on the X chromosome at Xq28.[36] Two other studies (Bailey et al., 1999; McKnight and Malcolm, 2000) failed to find a preponderance of gay relatives in the maternal line of homosexual men.[35] One study by Rice et al. in 1999 failed to replicate the Xq28 linkage results.[37] Meta-analysis of all available linkage data indicates a significant link to Xq28, but also indicates that additional genes must be present to account for the full heritability of sexual orientation.[38]

The new finding is consistent with multiple earlier studies of twins that indicated same-sex attraction is a heritable trait.

A new study suggests that genes are responsible for between 8% and 25% of same-sex preference.

The 2019 study is the latest in a hunt for “gay genes” that began in 1993, when Dean Hamer linked male homosexuality to a section of the X chromosome. As the ease and affordability of genome sequencing increased, additional gene candidates have emerged with potential links to homosexual behavior. So-called genome-wide association studies identified a gene called SLITRK6, which is active in a brain region called the diencephalon that differs in size between people who are homosexual or heterosexual.

Genetic studies in mice have uncovered additional gene candidates that could influence sexual preference. A 2010 study linked sexual preference to a gene called fucose mutarotase. When the gene was deleted in female mice, they were attracted to female odors and preferred to mount females rather than males.

Other studies have shown that disruption of a gene called TRPC2 can cause female mice to act like males. Male mice lacking TRPC2 no longer display male-male aggression, and they initiate sexual behaviors toward both males and females. Expressed in the brain, TRPC2 functions in the recognition of pheromones, chemicals that are released by one member of a species to elicit a response in another.

With multiple gene candidates being linked to homosexuality, it seemed highly unlikely that a single “gay” gene exists. This idea is further supported by the new study, which identified five new genetic loci (fixed positions on chromosomes) correlating with same-sex activity: two that appeared in men and women, two only in men, and one only in women.

How might these genes influence same-sex behavior?

I find it intriguing that some of the genes from men identified in Ganna’s study are associated with olfactory systems, a finding that has parallels to the work in mice. Ganna’s group found other gene variants that may be linked with sex hormone regulation, which other scientists have previously suggested plays a large role in shaping the brain in ways that influence sexual behavior.

Conditions in the uterus during pregnancy are thought to influence the sexual preferences of the child.

Males with a genetic condition called androgen insensitivity syndrome can develop female genitalia and are usually brought up as girls, despite being genetically male – with an X and Y chromosome – and they are attracted to men. This suggests that testosterone is needed to “masculinize” a prenatal brain; if that doesn’t happen, the child will grow up to desire men.

Similarly, girls who have a genetic condition called congenital adrenal hyperplasia are exposed to unusually high levels of male hormones like testosterone while in the womb, which may masculinize their brain and increase the odds of lesbianism.

It’s also possible that hormonal shifts during pregnancy could affect how a fetus’ brain is configured. In rats, manipulation of hormones during pregnancy produces offspring that exhibit homosexual behavior.