In principle, such matters cannot be kept from the family because an HIV carrier has to live with family members. Although the main modes of HIV infection are through blood and sex, but... no one can guarantee that daily contact won't lead to infection.
Although it's officially stated that HIV cannot be contracted through everyday life, that's not necessarily true. It can only be said that the possibility of infection through daily contact is very small, so small it can be ignored, but... family members have to live with an HIV-positive person every day, so the chances of infection... are actually quite significant.
Therefore, when Qiao Bing asked about Qiao Chuchu's situation, the doctor told him. The doctor was just a doctor; he didn't know about the complicated relationships of the Qiao Family.
