It was the custom of ancient royalty to recline on the left for two reasons:

a) Food is normally held in the right hand. Leaning toward the left leaves the right hand free.

b) Leaning on the right is a choking hazard. It can prevent the epiglottis from covering the trachea, allowing food to enter and stop the flow of oxygen.

Wishing you a happy and kosher Passover!

Rabbi Menachem Posner