When gas burns it uses oxygen up around it as in the fire triangle diagram we get taught needs ignition source,a fuel,and oxygen,its reason why when you install a gas fire over certain kW you need a air brick for ventilation in that room as flue gases rise up chimney and can draw in fresh air through the air brick in that room replenishing the air/ oxygen etc .
I live in England at momemt and as your wife doesn't like using the fan on your range,my mrs doesn't like or understand why I want window open just a little at night in living room,keep explaining over and over but often look the window and it's shut lol but it is November and is chilly so I get it ^_^