How do antibiotics create drug-resistant strains
There is no such thing as a "stronger" or "weaker" strain until the bacteria are treated with antibiotics.

It is true that potentially antibiotic-resistant mutants will still occur whether or not treated with antibiotics.

However, the mutants would not be "stronger" without the antibiotic use, so there is no selective pressure for them to survive to any greater degree than the wild-type. Without the antibiotic, something else will kill that mutant bacteria, meaning that the mutation ultimately did not make it any stronger.