The only way they justify this is by saying that it's safer than your child killing themselves. That's the only way you can justify any dangerous drug - are the side effects of the drug better than the thing you're using it to do.
Eg. The Pill - has side-effects, but safer than pregnancy. Vaccination - has possible side effects, but safer than the diseases themselves. Then you balance this risk/reward for the patient.
So someone with severe dysphoria, who's not got better with therapy, might go for surgery. Someone in continuous pain, will take strong painkillers that will probably eventually lead to their death.
And these puberty blockers are so dangerous, that the only way these people can justify giving them to kids is to say that the alternative is that the children will suicide - they're so dangerous, they have to go straight to death as the alternative to balance against.
And what's crazy about this, is there isn't even proof of this high rate of suicide specific to trans. Read any study, and there's a high rate of co-morbidity with other mental health issues, or with other reasons for increased risk of suicide (eg being gay or lesbian in an unwelcoming environment) - but rather than research this, or try to reduce the suicide risk in other ways (eg, the LGB - 'it gets better' campaign) it's used as a justification for damaging these kids with dangerous drugs.