Rotation of methylammonium (CH3NH3 or MA) molecules is believed to govern the excellent transport properties of photocarriers in the MA lead iodide (MAPbI3) perovskite. Of particular interest is its cubic phase, which exists in industrially important films at room temperature. In order to investigate the rotational behaviors of the MA molecules, we have performed ab initio molecular dynamics simulations of cubic-MAPbI3 at room temperature. There are two types of rotational motions of MA molecules in a crystalline PbI3 cage: reorientation of a whole molecule and intramolecular rotation around the C-N bond within MA molecules. Using a cubic symmetry-assisted analysis (CSAA), we found that the prominent orientation of the C-N bond is the crystalline ⟨110⟩ directions, rather than the ⟨100⟩ and ⟨111⟩ directions. Rapid rotation around the C-N bond is also observed, which easily occurs when the rotational axis is parallel to the ⟨110⟩ directions according to the CSAA. To explain the atomistic mechanisms underlying these CSAA results, we have focused on the relation between H-I hydrogen bonds and the orientation of an MA molecule. Here, the hydrogen bonds were defined by population analysis, and it has been found that, while H atoms in the CH3 group (HC) hardly interacts with I atoms, those in the NH3 group (HN) form at least one hydrogen bond with I atoms and their interatomic distances are in a wide range, 2.2-3.7 Å. Based on these findings, we have given a possible explanation to why the ⟨110⟩ directions are preferred. Namely, the atomic arrangement and interatomic distance between MA and surrounding I atoms are most suitable for the formation of hydrogen bonds. In addition to films, these results are potentially applicable to the rotational behaviors in bulk MAPbI3 as well, considering that the atomistic structure and time constants regarding the rotation of MA molecules statistically agree with bulk experiments.