An even simpler explanation is return to mean. They were going to get better in a few days anyway, with or without antibiotics. But if they keep getting antibiotics each time, they're always going to think that they helped. Confirmation bias comes in here too, why not.

What's even worse is that unnecessary use of antibiotics can affect someone's gut biome and leave them worse off for months, in some extreme cases years. I have had antibiotics only a couple of times in my life (for bleeding injuries) and I noticed the effect on my gut each time. To think that people create this problem when they don't have to is alarming. I hope for their sake their doctors _are_ prescribing them placebos so it's harmless ignorance.