Shortly after the powers that be declared that homosexuality was not a mental disorder, they proclaimed that dogma that it was also impossible to change. Prior to that, it was taken for granted among psychiatrists in the field that a cure for homosexuality was possible - difficult, time-consuming, and uncertain, to be sure, but definitely possible - and they had the case studies to prove it. Conversion therapy is neither new, nor restricted to religious zealots, not ineffective.
There is a certain irony which is never mentioned. The naysayers have never come out with a study whereby the therapy has been applied to a large number of conscientious patients, and found to be 100% ineffective. On the contrary, there is ample evidence of cure rates of the order of a third to a half of patients. Indeed, in a high proportion of cases, change is spontaneous. Whitehead and Whitehead devoted a whole chapter of their book, My Genes Made Me Do It (downloadable here) to both spontaneous and assisted change. Dr Spitzer, who was largely instrumental in getting homosexuality taken off the list of mental disorders, nevertheless, to his surprise, discovered that a lot of people had made successful changes. More detailed is that of Dr Phelan, who quoted 100-odd studies, some very old, some very new. I am glad I copied it when I first encountered it, because now it can generally be found on the net only minus the long list of references which gives it its value. For your information, therefore, I enclose the full review. I am sure he would not mind.