In eukaryotic cells, DNA is bound to nucleosomes, but DNA segments occasionally unbind in the process known as nucleosome breathing. Although DNA can unwrap simultaneously from both ends of the nucleosome (symmetric breathing), experiments indicate that DNA prefers to dissociate from only one end (asymmetric breathing). However, the molecular origin of the asymmetry is not understood. We developed a new theoretical approach that gives microscopic explanations of asymmetric breathing. It is based on a stochastic description that leads to a comprehensive evaluation of dynamics by using effective free-energy landscapes. It is shown that asymmetric breathing follows the kinetically preferred pathways. In addition, it is also found that asymmetric breathing leads to a faster target search by transcription factors. Theoretical predictions, supported by computer simulations, agree with experiments. It is proposed that nature utilizes the symmetry of nucleosome breathing to achieve a better dynamic accessibility of chromatin for more efficient genetic regulation.