dynamic drivers are stiff, light and comparatively large diaphragms with a voice coil in the center. The size of these are often 10X to the openings of a BA, this means that more air is moved. The feeling of deep bass is a result of the movement of a lot of air at speed, which requires a large diaphragm with enough force to move a large volume of air fast. Furthermore, your ear is better adapted to handling midrange frequencies, and things like subbass need to be played at a much higher volume in order for you to hear them, which requires even more air to be moved. A BA diaphragm is much smaller and cannot move as much air.
Think about a drum 10 ft across and a drum half a foot across. If hit with the same force, which will be able to produce more bass? No matter how hard you hit the small drum, you'd be hard pressed to get a similar bass response.
And for the others that may try to correct me, I know that it also has to do with resonant frequency, but understand also that bass production is much easier with a larger diaphragm.