Why do evolutionists think that resistant bacteria is proof of evolution?
antibiotic resistant bacteria or insecticide resistant pests are all examples of evolution.
Antibiotic resistance could be naturally present as unique variation in a few organisms within the bacterial population. Normally it does not provide any advantage to the organism, but if the organisms are exposed to antibiotic (against which some organisms are naturally resistant) then an advantage sets them apart from the rest of the bacterial population.
Resistant organisms survive ( survival of the fittest ) longer, and the nonresistant ones perish fast. The resistant bacteria get chance to multiply at higher rate ( differential reproduction ) and the resistant progeny bacteria flourish in absence of competitors i.e. nonresistant bacteria.
Frequency of genetic allele that provides resistance increase very fast in bacterial population. Eventually antibiotic resistant bacterial population appear. Whenever allele frequency in a population changes, the population is said to be evolving.
Such evolutionary processes also help us in understanding the fact that all adaptations appear as pre-adaptive characters (due to random mutation). In suitable environment, such pre-adaptive characters get selected.