Yes, Greer made a big point out of establishing that this state puts Terri firmly on the "not human" side and therefore she has no legal right to live. I have never heard of any law that states that someone who cannot meet some arbitrary definition of "human being" cannot be allowed to live.
Greer did not follow the law, he set precedent.
Now that the precedent has been set, there is no reason to continue taking care of the thousands of other people whose levels of consciousness are similar to Terri's. Who's going to get Greer or another heartless judge to order their executions? Maybe a taxpayer's group, upset that we spend so many billions on their care every year?
Your explanation of the case is not accurate.
Greer did not order Teri to be put to death.
He refused to interfere with medical decisions made by her next of kin, her legal guardian under the law.
There is an enormous difference.