Conflating the two purposes is what produces most bad advice on the subject, because they point in opposite directions for the same bottle.
Separating sediment
Old reds and unfiltered wines throw a deposit that is harmless but gritty. Stand the bottle upright for a day so the sediment collects at the base, then pour slowly and without stopping, and stop when the deposit reaches the shoulder. Stopping and restarting sends it back through the wine.
Aeration
The argument is that air softens a young, tight or reductive wine. The effect is real but modest, and the wide surface of a decanter does far more in ten minutes than a glass does in an hour. Whether a given bottle benefits is a judgement, not a rule.
The risk with old wine
A fragile old bottle can fade in air within the hour. Sediment is the reason to decant one; time in the decanter is not, and an old wine decanted early can be past its best by the time it reaches the table.
Opening the bottle early does almost nothing
The wine's exposed surface at the neck is a couple of square centimetres. Pulling the cork an hour ahead is very close to no aeration at all.