The 5th Amendment also says ..."nor be deprived of life liberty or property without due process of law..." The Supreme has ruled that a judge cannot sentence a person to death unless the jury has recommended that they be put to death. You may remember that many people had their sentences reversed on this ruling. So how can a person be sentenced to death without a jury trial. Unknown. But the police can also kill you and say that you were a danger to them and they will never be brought to trial, see the story about the invalid being shot in bed by an officer who invaded his house through a second story window and is given a 30 day suspension which he says he will fight. So all in all we have lost our freedoms to the judiciary and the police.
Short answer: because Florida law states that it is Michael Schiavo who is allowed to bring the lawsuit, and he didn't ask for one.
Now I went to school in the 60s and given inflation...