1: Straight-up natural selection
Bacterial population mostly commensals and symbiotes with a few pathogenic bacteria present, some resistant -> commensals and symbiotes keep pathogens in check through eating their food -> take antibiotics -> resistant bacteria, including resistant pathogens are suddenly favored -> now it becomes a real problem
2: Somewhat roundabout and downright insidious.
Infection false positive -> take antibiotics for nonexistent "infection" -> commensals and symbiotes forced to adapt (develop resistance) or die -> small chance some of them could encode antibiotic resistance in plasmids -> those plasmids might transfer and end up in the "wrong hands" (pathogenic bacteria) -> nice going "genius", you just spawned another infectious headache for everyone else.
Somewhat unrelated, even if the new plasmid doesn't happen, improper use of antibiotics can cause an infection anyway:
Infection false positive -> take antibiotics for nonexistent "infection" -> commensals and symbiotes die off -> large amounts of "food" (stuff that bacteria eat) left up for grabs -> finish antibiotic course -> bacteria repopulate -> chance of pathogenic bacteria grabbing more food first and crowding out commensals and symbiotes -> now you're actually sick