It’s not us that become resistant, it’s the bacteria we are trying to kill. Bacteria multiply quicker than other organisms and have simpler genomes, so random mutations happen more often. Some of those might give them a tougher cell wall or a way to metabolise a toxin.
Low doses of antibiotics given to farm animals, and as medicine to humans who don’t really need it, provide an environment that only kills the weaker bacteria. The ones that are left are those with the genes for antibiotic resistance, so they go on to multiply and spread those genes.