The short answer is because Squall doesn’t die.
The long answer has to do with the nature of Life and the role death plays in the narrative. So to answer this fully, let’s look at what Life in Final Fantasy VIII does:
Revives a target from Knocked Out status and restores 25% of their HP.
The game description for Life is “Revive from KO”. So then, Life doesn’t actually resurrect you from Death. When you fall in battle, you’re just unconscious. Life, in this sense, brings you out of unconsciousness, as if it were resurrecting you. I guess that if all of your characters fell in battle, your enemies would surely finish them off. But until that happens, your characters lay “lifeless” on the ground.
Labeling the “Death” status as “K.O.” was a tradition from the NES days to keep these games “family friendly”. You could kill (read: RUB) your enemies, and they could K.O. you.
Let’s say Squall really did die. Could Life resurrect him? No. If you’ve been dead, as opposed to having your heart dead, electrical cardioversion will do nothing but jump your nerves. Lifewise, if your characters are truly dead, Life won’t bring them back. This goes for characters who did die in their respective stories, such as:
- Josef in Final Fantasy II
- Tellah in Final Fantasy IV
- Anna in Final Fantasy IV
- Galuf in Final Fantasy V
- General Leo in Final Fantasy VI
- Cid Del Norte Marquez in Final Fantasy VI
- Shadow in in Final Fantasy VI
- Aerith in Final Fantasy VII
- Biggs, Wedges and Jesse VII
- Queen Branhe in in Final Fantasy IX
- Rasler in in Final Fantasy XII
- Reddas in Final Fantay XII
The role of their death is narrative, and most of the time magic doesn’t have an effect on the plot. It can, with casting Holy, Ice Strike or Bahamut, but usually not with killing or reviving characters.
This raises the questions: what about Death? What does it do as a magic spell? Since it insta-kills your enemy, you would think it does cause them to die. However, you can have it cast on your characters, and they still won’t die – only suffering a knockout. So then, whereas life wakes you up, death stops you and puts you in your sleep (not like Stop or Sleep, but practically they take the character out of battle). This assumes Death knows your enemies out too.
If you’re hungry for Behemoth meat, killing them in their sleep would give them a painless death.
My courtesies to the chef, Ignis.