The sexual abuse of children is not about sex. It is about power and control. Chemical castration would not stop a pedophile from abusing children. It would only give people a false sense of security that could very easily result in traumatizing even more children with sexual abuse at the hands of repeat offenders.
There is a long family history in many families of secrets about "Uncle Joe", a brother, a cousin, or grandfather who molested children. Because of ignorance and shame, it has only been in the past few decades that courts, law enforcement and social services have addressed the problem of the sexual abuse of children. To this day, in many families there is a reluctance to hold family members accountable for molestation. The act is minimized and dealt with with privately, sometimes by thinking they can simply keep the predator from offending again.
Imagine the danger if families and neighborhoods thought chemical castration would deter a pedophile from re-offending. The ugly truth of sexual abuse is that it is not driven by sexual gratification. It is driven by a need to have power and control over a victim. A pedophile, a person who is driven to repeated acts of child sexual abuse, may lose the ability to achieve sexual arousal or orgasm. It would not stop such a person from still performing sexual acts on a child. I will not give explicits but there is a huge realm of horrific acts that pedophiles violate children with. Chemical castration would do nothing to reduce that ability.
I much prefer more stringent laws of incarceration that would insure repeat offenders are never given the freedom to offend again. That would serve both the purpose of punishment and public safety. After all, victims of child abuse must live the rest of their lives dealing with the aftereffects of abuse. So, too, should the perpetrator.