well 50% of the results of any quantifiable survey are below average by most definitions of average. It's not a value judgement. It's a function of maths.
But yes, I guess that's why they use the definition they do, because most people take average to mean the norm, rather than an expression of a specific mathematical point on a scale.
If you were going to be uber pedantic you could say
"10% of people are below average intelligence but 50% of people fall below THE average". 
Interesting that your Dad clearly assumes he's on the right side of "average"!
There was a fascinating programme on More or Less, I think, where they looked at the "above average" phenomenon. Like, if you question people, about 70% of people consider themselves to be better than average drivers. Clearly this is not possible.
And about 50% of parents are in favour of grammar schools for their children, whereas most selective schools only take the top 20% of results. This means that the majority of parents in favour of grammar schools would actually find their children were not entitled to go.
It's also called the Lake Wobegon syndrome - from the Garrison Keiler stories. You know, Lake Wobegon, where all the women are strong, all the men are good-looking, and all the children are above average.