I think this has a lot to do with treating “smartness” as a one-dimensional continuum. Sure, you can measure things like IQ to get a generalized sense of one’s overall intelligence (though even that has its own problems) but it’s much more accurate to look at it as a collection of different skills and abilities. The brilliant writer might not be able to do simple math without a calculator. The master coder might be absolute rubbish at organic chemistry. Pick a couple dozen different skills and chances are nearly everybody’s above average in at least one or two.
What you’re good at shapes your conception of yourself and what’s important. You’ll value the skills you possess more than is strictly accurate. Plus the more you practice at it the better you’ll likely become over time. It’s easy to see how a lot of people convince themselves that they’re “above average” this way.
What are your above-average skills? Think of five. Mine are: