Why did Voldemort need to drink Unicorn blood?

Question

"[...] it is a monstrous thing, to slay a unicorn. Only one who has nothing to lose, and everything to gain, would commit such a crime. The blood of a unicorn will keep you alive, even if you are an inch from death, but at a terrible price. You have slain something pure and defenceless to save yourself, and you will have but a half-life, a cursed life, from the moment the blood touches your lips."

- Firenze, Harry Potter and the Philosopher's Stone

In the first Harry Potter book/movie, we found Voldemort drinking Unicorn blood. Why did he need Unicorn blood to stay alive? Maybe, unicorn blood works on an undead soul, but wasn't he already protected by his Horcruxes in terms of being kept alive?

Answer 1

Voldemort never drank unicorn blood through his face on the back of Quirrell's head. Instead, Harry sees Quirrell leaning over the body drinking the blood himself. During the graveyard scene in Goblet of Fire, Voldemort talks about how he still had the power to possess animals, but the animals all died shortly afterwards.

I sometimes inhabited animals — snakes, of course, being my preference — but I was little better off inside them than as pure spirit, for their bodies were ill adapted to perform magic… and my pos- session of them shortened their lives; none of them lasted long….

— Goblet of Fire, chapter 33 (The Death Eaters)

It's likely that by drinking the unicorn blood, Quirrell was preserving his own life.

Keep in mind that contrary to the movie, it wasn't Harry's attacks that killed Quirrell. He died because Voldemort fled his body:

“The servant died when I left his body, and I was left as weak as ever I had been,”

— Goblet of Fire, chapter 33 (The Death Eaters)

Firenze was right, he really was only an inch from death, and it was only a combination of unicorn blood and Voldemort's power that kept him alive.

Alternatively, unicorn blood was one of the ingredients in the potion that allowed Voldemort to take his weakened baby-like form before his body was fully restored. So it's possible that by drinking the blood, Quirrell was somehow allowing Voldemort to create a physical face.

Answer 2

See what I have become?' the face said. 'Mere shadow and vapour... I have form only when I can share another's body... but there have always been those willing to let me into their hearts and minds... Unicorn blood has strengthened me, these past weeks... you saw faithful Quirrell drinking it for me in the Forest... and once I have the Elixir of Life, I will be able to create a body of my own... (Philosopher's Stone)

He needs Unicorn blood to strengthen himself. Without it, as per Quirrel's worries, he was even weaker:

'Master, you are not strong enough!'
'I have strength enough... for this...'

Answer 3

The Horcrux kept Voldemort alive, in a ghost-like state where he wasn't able to do very much. When Quirell found him, he was able to have a body, but he was very much in a half-life, not able to do anything of significance. Eventually, that connection started to break down. The unicorn blood allowed Voldemort to continue to possess a body, in effect keeping him alive. Indeed, without the unicorn blood, he returned to the type of life he had previously, which wasn't really living life at all, as ended up happening eventually anyways.

Answer 4

It wasn’t Voldemort drinking the blood, it was Quirrel, to keep himself alive!

We see in COS that possession by Voldemort can be nearly fatal, as we find Ginny would have died if Voldemort had gained any more strength.

“So I made Ginny write her own farewell on the wall and come down here to wait. She struggled and cried and became very boring. But there isn’t much life left in her. . . ."

Also, referring to Quirrel himself (GoF)

"The servant died when I left his body, and I was left as weak as ever I had been,” Voldemort continued."

And this is stated explicitly in regards to animals:

". . . and my possession of them shortened their lives; none of them lasted long. . . ."

We also see in Fantastic Beasts that an Obscurus, which seems similar in many aspects to possession, destroys the host.

"There’s no documented case of any Obscurial surviving past the age of ten. The one I met in Africa was eight when she – she was eight when she died."

Thus, Quirrel, being possessed by someone with the strength of Voldemort, needed to drink Unicorn blood to keep himself alive.