Why should there be a different burden for opposing sides? I don't know, or care, if it is hard-wired. All I'm saying is that if one side wants to be believed, that side needs to present the proof. You confused the issue by the assumption that because the homosexuals claim that they think it's hard-wired, that we need to believe them because we can't prove it's not. I say that it is what it is and maybe someday science will be able to tell us what it is. I know some who appear to be hard-wired and some who are merely hedonists who go after any sort of pleasure they can get. If it matters to you, I say go ahead and try to enlist someone with the background and abilities to try to prove your side of the argument - it's a scientific matter and you cannot compare it to a legal matter where the prosecution has to do all the proving. It shouldn't even be a one side against the other issue - it should be a scientific interest just for the knowledge.
I can't think of any way a scientist could prove the assertion "Homosexuality is NOT inborn" any more than a lawyer can prove "Defendant did NOT commit the crime in question." (In the latter case, witnesses could be summoned that would testify the defendant was somewhere else and therefore COULDN'T have committed the crime, but that presupposes 1 - the witnesses aren't lying and 2- the time and place of the crime are truly established.)
On the other hand, if homosexuality IS inborn, then there would be ample evidence to support that assertion. However, almost none of the evidence (that's not merely anecdotal) does. In fact, it tends to DISPROVE it.
Logically, it does not follow that because I can't prove something does NOT exist, it must exist. That is a fallacy.