I am asking WHY the errors exist.
The atmosphere behaves differently to a sealed container.
The air is not contained by a solid boundary at the top - but is open (only earth's gravity keeps it in place.) The upper boundary can rise and fall with temperature variations whilst the surface pressure remains the same.
Hence any pressure sensing device (Altimeter) would indicate the same pressure (Altitude) at a lower height if the air below the Altimeter is colder than standard. (Air column has shrunk in length).