Commander Kinsey wrote

Doesn't giving a coronavirus vaccine to everyone increase
the chances of the virus mutating to avoid the vaccine?

Nope, it's the reverse of that, the virus can only
mutate in infected people and so the fewer that
get infected, the less the chance of it mutating.

So we should be using it sparingly.

Nope, we should be vaccinating as many as possible with
the best vaccines to reduce the number who get infected.