Do you wish to argue that my right to life justifies my stealing your food?
Not especially. Such conflicts of rights are resolved by superior force (unless superior cunning is used in the theft) . Absent an organized society, they are resolved more or less on the spot and in accordance with the will of the person who can bring the superior force to bear. In an organized society, such conflicts of rights may be resolved on the spot or later in accordance with the laws or customs of the particular society. (Of course this is still in accordance with the will of the person who can bring the superior force to bear because that force includes the resources of the society. But that person’s will by itself is not enough. )
Since we live in an organized society (sort of), make an argument as to why the laws and customs of an organized society should favor one right over another when a conflict of rights exists.