Offered friend antibiotic ointment for cut, but they refused and said it can sometimes cause more bacteria. Is this true or myth?

Antibiotic Usage. Yes, inappropriate or overuse of antibiotics, internally or on the skin can lead to antibiotic resistance and overgrowth of resistant bacteria. I recommend following the directions on any antibiotic cream of prescription exactly and only use antibiotics when clinically indicated.
Unlikely. If it is an antibiotic it probably kills most bacteria, but possibly not fungus or other germs. Also some people develop an allergy to certain types of antibiotics. If the cut is dirty, it could hold the bacteria close to the bloodstream to put any kind of ointment over it. Best to keep clean and dry, with a bandage or dressing, and apply heat on the top of the bandage to help speed healing.