This avoids a lot of dysphoria-provoking secondary sexual characteristics from progressing, and also avoids accidentally "transing" a cisgender teenager.
Nobody hesitates to give puberty blockers to cisgender teenagers, for other medical reasons. I knew a young girl who had to have puberty blockers because she had a precocious puberty and it was literally destroying her young body -- she was not old enough physically or mentally to be able to deal with it.
However, for whatever reason, there is a huge backlash against giving it to transgender teenagers, despite it representing the best and ultimate choice in self-determination -- "Take these for a few years and then when you are 18 you can decide which puberty you want to go through". It leaves room for the individual to decide. If the person decides against it before then, they can stop and puberty immediately resumes as normal.
When the suicide rates are as high as they are for transgender people, and there is the option of halting the things causing the suicidal feelings, the dysphoria, all of the physical and emotional and societal pain. Halting an onslaught of pain that is utterly soul destroying, and just giving them more time to make a choice and more of an informed decision, how can there be any empathically-cogent argument against that?