The concept can be simplified.
A fair coin has heads on one side and tails on the other. With a fair flip, there is 1/2 chance of the top face being heads and 1/2 chance of the top face being tails. So when we flip the coin, we should expect that the top face will be half heads and half tails. Yet every single time we flip the coin, it comes up just heads or just tails. On a single flip, we never, ever get the “normal” half heads and half tails. So you can’t “prove the normal” because it doesn’t exist. The top face will never be the "normal" half heads and half tails.
(You see, he is having a bit of a joke. April fools.)