There are a few flaws with your argument. This is probably a homemade copypasta that has thus far gone unchallenged because it is extremely TL;DR. but I'll dig into it.
This is just a minor error, but this is not a perfect definition. Schitzophrenics do not experience any "activity" or "desire"; hallucinations come to them without any active input on their part. I would add "or sensort input". This would also cover those faggy "indigo children" and other hippie shit.
But the greater issue here, is that under your very own definition, all the highly common and perfectly accepted psychological characteristics that I listed would be classified as "mentally ill".
Narcissism is debateable. Putting #1 first is the most direct path to survival, but it goes against human biological programming as a societal species.
Apathy would most certainly be a mental illness. Not wanting to do anything goes against the ability to survive and reproduce and therefore goes against biological fitness.
Introversion would definitely be a mental illness. Why would one have a higher biological fitness by losing energy from social interaction than by gaining energy from it? Or one could argue that drawing energy from loneliness is more fit for surviving independently, in which case extroversion has to be a mental illness. In a binary case like this, one of them has to be inferior.
So this begs the question, which you didn't address, is whether every variation in human behavior is some form of degeneracy. We should be different to some degree, for that's how we got the unique cultures of places like France, Germany, etc. So is there a cutoff limit for how much we can go against biological order before it becomes mental illness? Is homosexuality inherently beyond that border? After all, I did explain its use as a natural guard against overpopulation. This is the issue that I feel like Holla Forums hasn't really fairly addressed in depth.
Your definition of a "biologically necessary activity" is fine for lower-order organisms that don't have any complex emotion to speak of, but as the size of the brain increases, as it does in the great apes, humans, whales and the like, emotional health becomes a factor of survival, as it is the barrier against a wide variety of mental illnesses. As you can see by pic related, love/belonging is one of the most critical tiers of health beyond basic physical needs. Homosexuals merely satisfy that need by having intercourse with the same sex. Therefore, homosexuality falls within the guidelines of a biological necessity for all species dependent on emotional health.
So? Procreation is a problem right now, not a solution. Humanity will not be able to perpetuate itself if it dies of starvation. Homosexuality aids population growth by ensuring that the rate of growth does not surpass the threshold that the environment can support.