"Conversion therapy" is a controversial therapy used to "convert" gay people "back to straight." The process is almost always heavily influenced by religion, and can be very harmful, psychologically. Some gay people are forced into this against their will, by their parents. There have been cases where people have committed suicide or had suicidal thoughts.
The organizations who run the therapy are super sketchy as well.
Banning snake oil is never a part of a free society.
Whether you want to admit it or not, some people commit themselves to these centers and come out straight / believing they're straight/cisgendered/etc. Their motivations are generally because they come from a culture/family that is not accepting of who they really are. They themselves probably hate who they truly are. So they pay thousands of dollars for the chance of tricking themselves into believing that things are different.
Does it commonly fail? Of course.
But does there exist someone in the world who is living a happier life because they attended this therapy? I believe it's possible. And for that reason, I think banning it is wrong.
I imagine that choosing between being accepted by your community/family and being unhindered in expressing your sexuality is a very difficult and personal decision. I don't think any lawmaker has the right to make it for you.
> Banning snake oil is never a part of a free society.
The problem is parents forcing it on their kids. Set the minimum age to 22 or so (where most kids will be finished with college, since most kids are dependent on their parents for that now too), and it would be a lot more palatable.
I think it comes down to a game theory style argument. Most people who would undergo this would do so unwillingly by pressure from family, religion, etc. and face large downsides. The small minority that actually desires to do this are hurt by making it illegal, but the large majority that would otherwise be coerced into it are spared.
Many laws banning sexual practices are more justifiable under such laws. If society were different, such a law would be net negative, but instead it's a good idea. Thomas Schelling's "The Strategy of Conflict" talks a lot about ideas like these style arguments and I would recommend reading it. For example, it is often illegal to take or display a picture of your voting ballot, since making that universally illegal makes coercing votes harder.
That is a good argument for the existence of these laws, but anyway it is kinda strange that the LGBT movement promotes this kind of thing so enthusiastically. I don't imagine that people promoting these laws -- for example, the guy who made this website -- are aware of your argument.
The organizations who run the therapy are super sketchy as well.
Wikipedia has some extensive information on it: https://en.wikipedia.org/wiki/Conversion_therapy