I went to the doctors, I have acute bronchitis, why antibiotics for that, and not the common cold?

Bacteria vs virus. Te common cold is caused typically by a virus called rhinovirus. Antibiotics are not effective against viral illnesses.
Virus vrs. Bacteria. The public does not understand that mankind is going to disappear from infections resistant to antibiotics. The more we use antibiotics the more bacteria turn resistant to them. Colds and flu and acute bronchitis are caused by viruses and not bacteria. The treatment is supportive with over the counter medications. Fear of complications like early bact.Pneumonia trigger the drs to give antibiotics.
Antibiotics. Antibiotics only work on bacteria, not viruses. There are many types of cold viruses, by the way.
Bacteria vs Virus... Acute bronchitis is due to an infection of the airways and may be due to a bacterial infection and this is treated with antibiotics. On the other hand, the common cold is due to a viral infection and so antibiotics are ineffective. Antibiotics are effective against bacteria but not viruses.