Final answer:
Doctor Purita is concerned about the negative reputation (stigma) linked with administering HGH to athletes due to its controversial use for performance enhancement in sports.
Step-by-step explanation:
When Doctor Purita says he doesn't want to give HGH to his professional athletes because he doesn't 'need the stigma and that kind of reputation,' he is referring to the negative connotations and potential backlash associated with the use of Human Growth Hormone (HGH) in sports. The use of HGH for performance enhancement is controversial and often associated with cheating and unfair advantage in athletics. Doctor Purita wants to avoid being connected to these negative aspects, which could harm his professional standing and lead to legal or ethical consequences.