The irrationality you are referring to is called the self-serving bias (SSB). I wrote a thesis on overconfidence for my master in behavioral economics, and the two are related. SSB is a well-documented bias. For instance, 90% of American drivers think they are in the top 50%. It's hard for people to fully appreciate this fact. Allow me to illustrate. Do you still consider yourself, even after reading this statistic,…
Accident frequency is a power law distribution - a large percentage of crashes are caused by a small number of drivers who habitually violate traffic laws, drive drunk, or otherwise engage in risky behavior. One of the distinctive features of power law distributions is that there's this long tail of people with very small values, and then a few people who make up most of the curve. So (made up numbers) you might have 60% of the population who has never gotten in an accident, then 35% who has gotten in one, then a tiny fraction of 1% who's been in a dozen. Over an 80 year lifetime, that 6 million accidents/year results in 480 million accidents, or 2/person, so with the hypothetical percentages above, 95% of people are above the mean and 60% are above the median.
Just goes to show that you can't assume everything is a Gaussian. ;-)
A similar phenomenom occurs in many, many other fields. The average (median) wage-earner actually makes below average (mean) wages, because the existence of Bill Gates and Carl Icahn skews the distribution upwards. The median sale price for a startup is $0, because over half of them fail. The average test scores in Palo Alto or Weston, MA or Hunter College High School really are above average, because those places already preselect for bright kids. It's quite possible for Lake Wobegone to exist: you just need to compare your kids with someone else's average.
And none of this invalidates SSB, but you picked a bad example to illustrate it. When 90% of drivers think they're in the top 50%, they're right.