Earthing a conductor

The electrical potential has a gauge freedom because we can arbitrarily set the zero anywhere we want. This is because we can only ever measure differences in the potential and not the absolute value of the potential.

Conductors that are earthed are all at the same potential (because they are earthed to the same planet) so it is usually convenient to choose this as our zero. Any potentials that we measure are then the difference from the potential of the earth.

Note also that "Earth" or "Ground" in a circuit may not even be phsyically connected to the real Earth (the planet), but instead refers to the common point from which zero volts is defined

"why is an earthed conductor always at zero potential"

Because that's the definition. But we could have chosen any other number too. Voltage is a relative measure between two values, not an absolute value.

Think about length. When I say "12 feet", what does that mean? It means 12 feet from one point to another. We simply pick one of those points to be zero. Maybe we use Mean Sea Level as one end, or maybe the floor of your house, or maybe a completely arbitrary point we call "the datum". We just pick something to be zero because for that particular example it's convenient.

And nothing says convenient in voltages like "stick wire in dirt". So we call that zero.