The dry cabin air is a result of heating extremely cold air. As a human you feel mostly the relative humidity, from a technical standpoint you have to deal with absolute humidity.
With increasing temperature the amount of water tjat the air can hold (100% realtive humidity) rapidly increases.
If you take outside Air of -50°C and 100% r.h. and heat it up to 20°C, you end up with less than 10% r.h. while the air still contains the same amount of water.
This digramm shows the relation (unfortunately it ends at -20°C)
Additionally you cool down the (hot) bleed air in the ACP, so some water condenses there and is extracted to avoid icing of the heat exchanger. So you reduce absolute humidity when cooling the engine bleed air, before you put it into the cabin.
As the airframe structure gets really cold in flight, a lot of moisture from the cabin air (comming from the passengers) condenses there and accumulates in the bilge. It is impressive what ammount of water is drained from a 50 seater after an 2 hour flight !
There have been tests with moisturing the cabin air, but this leads to dramatic ammounts of condesion water in the bilge and on a lot of systems, so it was stopped.