Physics Question: Why does cabinet volume matter so much to bass response?

In simple physics terms, the woofer can woof more when the cabinet is bigger or is ported or a passive radiator is used.

Are you guys saying that a woofer can extrude further into the room and therefore play louder in a larger cabinet?  Is that because the air pressure is lower in a larger cabinet, so it pulls less on the woofer as it moves foward?

Well, it is a marriage between the driver and its abilities, and the cabinet made for it. You play to that particular drivers' strengths. In general, the bigger the woofer the bigger the cabinet. Again, this is applying to sealed and bass reflex/ported designs.

 It isn't a matter of the woofer being able to play louder any more than the woofer is supported by the cabinet's extension of resonance that aids in the woofer's lower octave response.

  You want big low bass, you will be the most successful with a larger cabinet and driver, given a proper design. And then you will move air.

You have to brace the heck out a large cabinet though, or else it will vibrate too much and the bass will be crap. A lot of smaller subs with strong cabinets can yield some amazing results.

Newer designs like the Devialet Phantoms manipulate Hoffman’s Iron Law using DSP and crazy amounts of power to get bass in small enclosures.