Many transgender people choose to medically transition, undergoing procedures such as hormone therapy and face/chest/genital surgery. For those who choose to medically transition, these procedures can alleviate gender dysphoria and increase quality of life. There are some risks to medically transitioning, such as complications or wanting to detransition in the future. Transgender adults are capable of assessing these risks and comparing them to the potential social and mental health risks of not transitioning. On the other hand, letting transgender children and adolescents medically transition has been a controversial topic. Though trans minors generally only have access to puberty blockers and hormone treatments (minors are not allowed to get genital surgery, and other surgical interventions are rare), choosing to undergo these treatments is still a big decision with possible risks. Yet, the health benefits of medical transition for some trans people are undeniable.
Yes, transgender children and adolescents should medically transition
If a transgender child or adolescent wants to medically transition, and they are insistent and persistent about their gender identity for an extended period of time, they should medically transition.
Medically transitioning has less health risks than not treating gender dysphoria
Transgender children and adolescents are at higher risks for depression, anxiety, and suicide than their peers, but social support and transitioning helps alleviate the gender dysphoria that causes those conditions. Transgender children and adolescents should be able to medically transition if they so choose because it is immensely helpful to their mental health.
Transgender children and adolescents should medically transition, but only once they begin puberty
Some studies have shown that transgender kids who claim to experience gender dysphoria before puberty may outgrow their gender dysphoria. The rate of "outgrowing" gender dysphoria greatly decreases after puberty.
The child/adolescent may not actually have gender dysphoria
Gender dysphoria and mental illnesses like depression and anxiety have overlaps in some of their symptoms. Additionally, prepubescent and pubescent minors may feel resistant to their assigned gender's gender roles for reasons other than gender dysphoria. Because these separate issues can be mislabeled as gender dysphoria by minors, minors who think that they may be transgender should not medically transition.