Why doesn't a brick slide more easily on its narrow side?

A brick doesn't slide more easily on its narrow side because the surfaces never really touch over their whole area anyway. Look closely enough and even a polished surface is a landscape of tiny bumps, called asperities. Two objects only truly touch at the tips of those bumps, a tiny fraction of the area that seems to be in contact. What sets that true contact area is how hard the surfaces are pressed together, not how big they look.

Put the brick on its wide face and its weight is spread over many bumps, each lightly squashed. Stand it on its narrow edge and the same weight presses on fewer bumps, squashing each one more. The total true contact ends up about the same, so the friction does too. That is why the friction force grows with the load but ignores the apparent area.

The first person known to notice this was Leonardo da Vinci, who wrote down the laws of sliding friction in 1493. But his notebooks were not published, and the laws stayed unknown until Guillaume Amontons rediscovered them in 1699. Only in 1950 did Frank Bowden and David Tabor show directly why they work: real contact is a small fraction of apparent contact, and it grows with pressure.