Because he did not die. Fawkes the friendly phoenix used his tears to heal Harry's arm before the venom was able to kill him. If he was killed by the venom, then at that point the horcrux inside him would've died.
Harry Potter was wounded by the venom and would have died if Dumbledore's phoenix Fawkes hadn't shed healing tears upon him, but the fact that he was healed also prevented the Horcrux inside him from being destroyed.
The Basilisk could only be controlled by the Heir of Slytherin, Tom Riddle. Other Parselmouths (such as Harry Potter) had no control over her, though they still could understand her. Aragog (a rare Acromantula) was accused of being the monster of the chamber by Tom Riddle which sent Hagrid to Azkaban.
When Tom Riddle commanded the Serpent of Slytherin to attack Harry Potter, he was seemingly unaffected by the Basilisk's gaze. If the Basilisk's eyes were damaged (thus rendering it blind), it took away the lethal ability as well.
How will professors react if you use Avada Kedavra in front of them - Hogwarts Legacy
Could the basilisk kill Harry?
Tom Riddle described the venom as being able to kill Harry in a little more than a minute, though Fawkes's tears healed Harry's arm and cleansed the poison. After being healed, Harry took the fang and stabbed Riddle's diary, destroying that Horcrux beyond magical repair.
Harry Potter, Ron Weasley, and Gilderoy Lockhart came to the rescue. Ron and Lockhart were stuck behind an avalanche of stone, so the battle was fought mostly by Harry. Harry managed to defeat both the Basilisk and the memory of Tom Riddle, thus saving Ginny's life.
Why didn't Harry use Parseltongue to control the Basilisk?
Of course, at that moment, Harry Potter didn't know there was a piece of Voldemort's soul in him, so he wouldn't have even tried to communicate with the Basilisk, but had he tried and succeeded at it, Harry Potter and the Chamber of Secrets would have ended very differently.
Harry, as heir of Gryffindor, possessed the love of this Muggle-born woman in his very blood and was the perfect champion to stand up against the heir of Slytherin.
When Nagini bit Harry at Godric's Hollow while coming out of her disguise as Bathilda Bagshot, it is unknown how dittany was capable of stopping the bleeding, when Arthur and Snape both bled unstoppably, with Snape actually dying from it.
Riddle summons the basilisk after Harry expresses his support for Dumbledore, which in turns summons Fawkes, who blinds the basilisk, allowing Harry to look at it directly without being killed or petrified.
Well as explained in the book in order to destroy a horcrux you need to destroy in such a manor that it can't repair/heal itself with magic, Basilisk venom is one of the few things that fits this bill: aside from Phoenix tears and maybe a bezoar there are no known cures and unlikely build in its defense mechanism.
How did the Basilisk Fang not destroy Harry's Horcrux?
Because he did not die. Fawkes the friendly phoenix used his tears to heal Harry's arm before the venom was able to kill him. If he was killed by the venom, then at that point the horcrux inside him would've died.
As a Parselmouth, Harry can easily communicate with Basilisk but I don't think he could controlled it as if he has the Basilisk under his will (or make it loyal to him) but more like he can influenced its behavior and take advantage to defeat it. Yes. Harry could have controlled the snake with Parseltongue.
How did Harry survive Avada Kedavra in the forest?
The Elder Wand, which Harry mastered, protected him during the Battle of Hogwarts and prevented Avada Kedavra from killing him. Voldemort's use of Harry's blood inadvertently kept Lily's protective charm alive and allowed Harry to survive the Killing Curse in the forest.
Ron, Mrs/Mr Weasley, McGonagall, Ginny, Dumbledore, and Harry were in the room when Harry explained how he had killed the Basilisk. Hermione probably knows since she figured out the Basilisk, so I guess she's gonna hear Harry killed it later. That gives us just a handful of people.
It's also lucky for Tom that Harry was a living thing that Fawkes could heal." JK Rowling also answered the question in an old blog post of hers. She said, “A Horcrux can only be destroyed if its container is damaged beyond repair. Harry was healed by Fawkes.
Newt Scamander classified the basilisk as a wizard killer that couldn't be domesticated. Yet, Herpo was able to control his. This had nothing to do with the fact that he was the breeder, and Harry Potter proved that being a Parselmouth wasn't enough - it must have been a Horcrux.
Basilisk was Slytherin's monster, who can be controlled only by his descendent. Tom riddle was his direct descendent. While Harry got his ability to speak parseltounge because he had a part of Voldemort's soul in him.
Can Harry still speak Parseltongue after he kills Voldemort?
After Lord Voldemort destroyed the fragment of his soul residing in Harry, Harry seemingly lost the ability to speak Parseltongue, about which he was glad and relieved. Over the next twenty-two years, he never attempted to speak the language, presuming that it had died with Voldemort.
A rare language spoken by a small number of wizards allowing them to communicate with snakes, the ability to speak Parseltongue was usually inherited with the majority of speakers descended directly from Salazar Slytherin.
Why Is Ginny Weasley So Powerful? J.K. Rowling once explained that Ginny Weasley is so powerful because she is the seventh child of a seventh child. This is part of folklore that has been around for a long time.
I find it most likely that Tom thought Ginny's soul was perfect because she was so young and innocent and had lead a very sheltered life, always protected by her family. This made her both very willing to trust Tom and very unwilling to believe that he was using her to attack her fellow students.
