Because some of the bacteria remain. Not enough to make you feel unhealthy. Enough to breed and spread. These survivors are the ones that were most resistant to

Because some of the bacteria remain. Not enough to make you feel unhealthy. Enough to breed and spread. These survivors are the ones that were most resistant to the antibiotics. Now they have less competition. They will breed more bacteria. More bacteria who inherit their improved resistance to antibiotics. Some of their children will be even more resistant. Some of their children will end up in someone else who, just like you, did not finish the course of antibiotics and, just like you, ended up being an incubator for a hardier, more antibiotic resistant strain. Eventually, the children are completely resistant and they laugh in the face of antibiotics, and then people start dying. People you never met. People who might be generations down the line from you infected with a super-resistant strain that can be traced back to you and others like you.