Does it actually cause harm?
In a very scientific report from American Psychological Association Task Force on the Appropriate Therapeutic Responses to Sexual Orientation, the question of
Are SOCE harmful?
Note that the scientific report has explicitly said:
In our review, we considered only peer-reviewed research, in keeping with current standards for conducting scientific reviews (see Khan, Kunz, Kleijnen, & Antes, 2003), which exclude the grey literature and lay material.
Their report reviewed many experiments, they are summarized here:
Early research on efforts to change sexual orientation focused heavily on interventions that include aversion techniques. Many of these studies did not set out to investigate harm. Nonetheless, these studies provide some suggestion that harm can occur from aversive efforts to change sexual orientation.
In the study conducted by Bancroft (1969) , he reported the intervention had harmful effects on 50% of the 16 research subjects who were exposed to it. Quinn, Harrison, and McAllister (1970) and Thorpe et al. (1964) also reported cases of debilitating depression, gastric distress, nightmares, and anxiety. Herman and Prewett (1974) reported that following treatment, their research participant began to engage in abusive use of alcohol that required his rehospitalization.
In McConaghy and Barr’s (1973) experiment, 1 respondent of 46 subjects is reported to have lost all sexual feeling and to have dropped out of the treatment as a result. Two participants reported experiencing severe depression, and 4 others experienced milder depression during treatment. No other experimental studies reported on iatrogenic effects.
None reported on adverse events.
Some recent studies document that there are people who perceive that they have been harmed through SOCE (Beckstead & Morrow, 2004; Nicolosi et al., 2000; Schaeffer et al., 2000; Schroeder & Shidlo, 2001; Shidlo & Schroeder, 2002; Smith et al., 2004), just as other recent studies document that there are people who perceive that they have benefited from it (Beckstead & Morrow, 2004; Nicolosi et al., 2000; Pattison & Pattison, 1980; Schaeffer et al., 2000; Spitzer, 2003).Many participants in studies by Beckstead and Morrow (2004) and Shidlo and Schroeder (2002) described experiencing first the positive effects and then experiencing or acknowledging the negative effects later. Among those studies reporting on the perceptions of harm, the reported negative social and emotional consequences include self-reports of anger, anxiety, confusion, depression, grief, guilt, hopelessness, deteriorated relationships with family, loss of social support, loss of faith, poor self-image, social isolation, intimacy difficulties, intrusive imagery, suicidal ideation, self-hatred, and sexual dysfunction.
Studies from both periods indicate that attempts to change sexual orientation may cause or exacerbate distress and poor mental health in some individuals, including depression and suicidal thoughts. The lack of rigorous research on the safety of SOCE represents a serious concern, as do studies that report perceptions of harm
So, there is a correlational link between "conversion therapy" and "harm" but not a causal link. Note that this is not a question of whether "conversion therapy" works or not, but only whether it causes harm.