They tell us that suicide is the greatest piece of cowardice... that suicide is wrong; when it is quite obvious that there is nothing in the world to which every man has a more unassailable title than to his own life and person.

This quote is saying that suicide is wrong because everyone has an unassailable claim to their own life and person. In other words, it is wrong to take away your own life because it is your right as a person to have and keep it. It is also described as the greatest piece of cowardice, suggesting that it takes a certain degree of fear or lack of courage to choose to end your own life.