Foreign-body aspiration favours the right side, and the reason lies entirely in comparative bronchial anatomy.
The right main bronchus is the $\textbf{wider}$, $\textbf{shorter}$ and more $\textbf{vertical}$ of the two; it descends almost as a straight continuation of the trachea. Gravity and the airflow path therefore deliver inhaled objects preferentially down this near-vertical pipe. The left main bronchus is narrower, longer and more horizontal because it must arch over the heart and aortic arch, so it catches debris less often.
On the parenchymal side, the right lung is divided by oblique and horizontal fissures into $\textbf{three lobes}$ (superior, middle, inferior), while the left has only two lobes with the lingula representing the middle-lobe equivalent. In an upright, conscious patient an aspirated object typically ends up in the posterobasal segments of the right lower lobe.
Putting the bronchial features together:
\[\boxed{\text{Wider} + \text{shorter} + \text{more vertical bronchus};\ \text{right lung} = 3\ \text{lobes}}\]