The gemara darshens that the permission is given to doctors to heal. Why do they need permission? What is it coming to exclude? Both Rashi and Tosafos say that it is coming to exclude the possibility that we view the illness as a gezeira from Hashem, and a human being who would try to heal would be undermining the gezeiras hamakom. However, Rashi implies that this would be a concern regardless of whether the injury was caused by human accident or by an illness beyond human control, whereas Tosafos says that this would only be a concern by illness that was not brought on by a human accident. Nonetheless, the Torah says that the doctor is given permission to try his best to heal. The Ramban in Torah HaAdam offers another approach, that a doctor could legitimately be concerned that he will mess up and cause the person to die sooner. The Torah is teaching that the doctor should not abstain, rather ther "permission" is given to medical experts to try, even though they may mess up. Both the approach of Rashi and Tosafos, and the approach of the Ramban, understand that the term "reshus" doesn't exclude a mitzvah, because it is surely a mitzvah. The term reshus is just to exclude one of the 2 possibilities above.
Based on the Ramban's approach that a doctor should take the risk, even though if he messes up he will cause the patient to die sooner, he asks a question on the gemara in sanhedrin 84b that says a person should not pop a pimple to remove the puss for one of his parents because he may cause a wound which would be a chiyuv misah. Just as one should not enter into a situation where they may inadvertently cause a wound to their parent, they should also not enter a situation where they may inadvertently kill someone? In the Ramban's first approach he explains that when it comes to removing splinters or popping a pimple, there is a definite advantage to someone else doing it rather than a child because for someone else it is not a chiyuv misah if they cause a wound, but for the child it is. However, something like blood letting where the injury itself is considered productive, it is not considered a chavala at all and is permitted even for a child. Regarding the concern that if too much blood is taken the patient may die, there is also no difference between a parent and a child because one way or the other the doctor will be entering into a safeik misah situation, but it has to be done. Based on this approach of the Ramban the only time a child must be makpid not to serve as a physician for his parent is when it is a minor procedure where there is a concern that he will make an chaburah that is not necessary for healing. But a major surgery would be permitted because regarding the chaburah, it is not considered a chaburah since it is the act of healing itself, and the concern of inadvertently killing the patient is the same whether it is a stranger or a child.