Scratch

State and local statutory regulations prohibit it from simply remaining here alone and companionless. You must euthanize it.

Let's take another look at this. This is referring to the companion cube, but if there was "state and local statutory regulations" that forbid things being "alone and companionless", replace it with GLaDOS. GLaDOS is not a lifeform (I will explain it later on).

Then:
In the song still alive you'll notice for the end, the first still alive is: G A A A.
However, for the second and last one, it is G F F F. It doesn't take a genius to figure out for the first time it is getting higher from STILL. However for the second time, it is different - downbeat and quiet.

Now look at the name Chell. What is the meaning? Daughter/Sheep.

For the final boss fight, if GLaDOS does not wish to be killed, you don't go and teach the player how to use rocket sentries to their advantage. Given that GLaDOS can say that test chamber 17 is under maintenance, she can do the same for the rocket sentries part.

Now what I'm thinking is maybe that GLaDOS was programmed to be unable to kill herself. She found a loophole by making someone want to kill her (which failed, and you know that because of the ending of still alive, downbeat and quiet).

Also, the companion cube. GLaDOS want Chell to be attached to the cube by referring it often, and then forces her to euthanize it, which is later used to destroy cores of GLaDOS. Again, you don't teach someone how to kill you unless you want to die. It also drives the player to want to kill her.

Let's look at when you're going to go in fire. There are people who completed the test chambers before Chell, as you can see by the writings and signs. Given that in Portal 2 glados have changed parts of test chambers, why don't she make the whole place dark walls so you can't place a portal on it?

Unless you want Chell to kill GLaDOS.

Then read Ayn Rand’s The Virtues of Selfishness:
“It is only a living organism that faces a constant alternative; the issue of life or death. Life is a process of self-sustaining and self-generated action. If an organism fails in that action, it dies; its This is unrelated, but please include assassin in your post so I know who is reading the whole thing. Thanks! chemical elements remain, but its life goes out of existence. It is only the concept of ‘Life’ that makes the concept of ‘Value’ possible. It is only to a living entity that things can be good or evil.
To make this point fully clear, try to imagine an immortal, indestructible robot, an entity which moves and acts, but which cannot be affected by anything, which cannot be changed in any respect, which cannot be damaged, injured, or destroyed. Such an entity would not be able to have any values; it would have nothing to gain or to lose; it could not regard anything as for or against it, as serving or threating its welfare, as fulfilling or frustrating its interests. It could have no interests or goals.”
Despite tossing her in a fire and that, GLaDOS still survived, which means that she:
1. Is not a living organism
2. Indestructible
therefore having no value, nothing to gain or lose, no interests or goals which means that:

1. The programmers of GLaDOS failed.
2. The experiments are not for science.

Not for science? It's to make someone(chell in this case, the 'rat-man' before) kill her, which sadly is impossible. In still alive:
Quote:
You just keep on trying till you run out of cake
That fits here. You just keep on trying to kill yourself until you run out of cake. But since there is no cake, you don't have anything to run out of. So you just keep on trying to kill yourself. Or GLaDOS is bored.