This is confusng 'mutation' with 'evolutionary changes'. Evolution is mutation followed by natural selction; it is not merely mutation.
Natural selection explains why creatures become extinct, not how they allegedly evolve.
Natural selction most certainly explains why bacterial populations develop antibiotic resistance.
We observe extinction occuring all the time, but never observe evolution.
It will be ironic if you happen to contract a multiply-resistant bacterial infection, because you'll have been killed by what you claim has never been observed.
Has there ever been a period in history when evolution occurred faster than extinction?
Do you have proof of such a period occurring, or do you simply assume that it must have occurred because otherwise evolution can't be true?
Why would single celled organisms, over time, evolve into things such as whales or dinosaurs when single cells are more fit to survive, and can in fact easily mutate to remain survivable?
I'm just asking questions here as a layman! :-)