It does. The animals will be colonized by bacteria that have "learned" to deal with all those antibiotics you gave. That resistance is easily transmitted.

I understand the problem with antibiotic resistance, but telling a farmer that an animal treated by antibiotics can't enter the food supply until after treatment ends doesn't really solve the problem when it comes to animals raised as food -- the farmer can treat the animal with antibiotics for nearly all of its life, only stopping the treatment just before slaughter.

Totally agreed. I'm naive to much around Ag/Husbandry. If that's what farmers do, that is a concern. From a microbiology point of view, the concept that "washing out" the drug before slaughter improves anything is flawed. It will be a reservoir of smoldering antibiotic resistance as long as that practice persists.