Why does the inside of my windshield fog up so quickly?

Interior fogging happens when warm, moist air meets cold glass, but a dirty inner windshield fogs faster because the residue film gives moisture more to cling to. Off-gassing from plastics, smoke and fingerprints all add to that film. Clean the inside glass thoroughly, use the air conditioning to dry the air, check that the cabin air filter is not clogged, and remove wet mats or items that add moisture.

References
  1. Dew Point vs Humidity, National Weather Service (NOAA)
  2. Factsheet 3: Water in the Atmosphere, Met Office (UK)
  3. Dew point, Wikipedia
Detailing Dictionary87 technical terms explained in plain English, from beading to wet sanding. Open the dictionary