B, mitochondria are related to breathing. Mitochondria are energy converters contained in both plant cells and animal cells. Mitochondria are places for breathing, releasing chemical energy stored in organic matter and providing energy for cell life activities. B correct;
C, the nucleus is the genetic information base of cells, which contains genetic material and stores the main genetic information of cells. C error;
D, the cell membrane controls the entry and exit of substances inside and outside the cell and maintains the normal shape of the cell. D error.
Therefore, choose: B.