See, the logic I heard re: resistance is the opposite. An infection is only an infection when the bacterial levels are high enough to cause symptoms. Anything below that is definitionally at a level where your body can at worst manage those bacteria without triggering symptoms. You can still be contagious, though.

So, when you don't finish your antibacterial regimen but instead stop when you feel better, you are maximizing the culture size of bacteria with some resistance, creating maximal chance for some resistant bacteria to spread. Finishing your regimen kills the most amount of bacteria; yes, the surviving ones at this point are the most resistant, but are at a small enough number that propagation and spread are far less probable.