Question

why are antibiotic not helpful for treating the common cold

Answer 1

Antibiotics, are helpful for treating the common cold, however due to them being very powerful medicine, they are not highly recommended. 

Answer 2

Antibiotics only work against infections caused by bacteria, fungi and certain parasites. They don't work against any infections caused by viruses. Viruses cause colds, the flu and most coughs and sore throats.