The phrase "you are a lot safer in an aircraft than in your car going to the airport" is misleading.
Virtually all car accidents are the result of driver error a high proportion of which are alcohol related. Car drivers are of mixed ability, age and health. Deaths on the road due to car structural faults or environmental issues are so rare as to be non-existent. Car accidents are predominantly non fatal.
It would appear to me that over the last few years passenger most aircraft accidents have been caused by bad decisions made by highly trained, medically fit people.
As a happy flier as long as I have the stick, but nervous commercial passenger, I am aware that flying is inherently safe because I trust guys like most of you. However this does not stop me from feeling nervous every time I board a commercial flight. It seems that I share this with many many others and no amount of statistical information will change this.
As far as cockroaches are concerned...get me out Scotty!