[PL 431] Choosing when to die?

What do you think about the following analogy?

newborn baby : birth :: terminal patient : death

1. A newborn baby is a human being who cannot choose whether to be born or die.
2. A terminal patient is also a human being who cannot choose whether or not to be born.
3. Therefore, a terminal patient should not be able to choose whether or not to die.

Just as humans do not choose when to be born, the argument goes, they should not be able to choose when to die. Is this a strong argument?