Why did Dumbledore not tell Harry that he was a Horcrux? It appears that Dumbledore was afraid of Voldemort finding out that he knew about the Horcruxes. At the end of Deathly Hallow Harry realized that Dumbledore also did not want to waste anyone else's life.
Dumbledore knew that destroying Voldemort's horcruxes was the only way to truly defeat him. He believed that Harry was the one person who was smart, courageous, and perhaps lucky enough to find and eliminate all the horcruxes.
He was sure there were Horcruxes after laying a eye on the diary (or at least started to think Voldemort might have them). What we, however, do know is that by the time book 4 came along, Dumbledore knew that Voldemort had Horcruxes and he also knew Harry would have had to die - expect this had changed.
He finds out for sure immediately after Nagini's attack on Arthur Weasley. This night is significant in many ways. While Harry sleeps, he enters Nagini's mind.
First of all, Dumbledore didn't reveal the secret of horcruxes to Snape because he didn't find it necessary. It wasn't his style to let out unnecessary secrets to people. Making horcruxes to fight horcruxes wasn't the plan.
Voldemort wasn't aware of Harry being a pseudo-horcrux because he didn't plan it, and Harry didn't know either until Voldemort “killed” him, but he actually killed the piece of soul kept in him.
In order to conjure the avada kedavra curse, you have to want to kill your victim. We all know that Voldemort could easily kill a child without an ounce of remorse... but not Snape. Snape didn't want to kill Dumbledore, and this was why the spell was blue instead of the usual green.
Voldemort intentionally made six Horcruxes, but when he used Avada Kedavra on Harry, he unintentionally created a seventh Horcrux. Instead of dying, Lily's love for Harry created a counter 'curse' known as Sacrificial Protection and saved Harry.
The Secret Horcrux — Harry
Voldemort's soul splintered then, killing his physical body and splitting his soul into a new Horcrux. Since he had just murdered Harry's parents in cold blood and attempted to kill a defenseless infant, there was enough justification for the creation of a Horcrux.
One is that Severus Snape is a master of Occlumency and therefore a difficult target for Voldemort to see through. The second is that Harry himself was not able to block Voldemort, and therefore the overall plan between Snape and Dumbledore was too critical to risk its discovery.
Dumbledore wonders if one of the remaining two Horcruxes belonged to Ravenclaw, since Gryffindor's only known relic, the sword, is safe in Dumbledore's office. Dumbledore believes that Nagini, the snake, is the sixth.
Dumbledore reveals how thoroughly he loves Harry. Harry is brave, and Dumbledore is proud as any father would be. More than that, Dumbledore succumbs to a parent's weakness; he cares more about Harry's happiness and wellbeing than the wizarding world he is trying to protect.
Additionally, when Harry touches the ring, there is a flash of images as the ring reacts to him, which Dumbledore explains as an identifiable trace of lingering Dark magic.
So why wasn't the Horcrux residing in Harry's head destroyed when he was bitten by the Basilisk? The answer is simple: He didn't actually die. Fawkes quickly healed the bite wound with his phoenix tears just in time. Case closed.
“Dumbledore didn't want to lose his wand at that point and Draco disarmed him. So that meant that the wand gave Draco its allegiance, even though Draco never knew it, even though Draco never touched it. “From that moment on, that wand gave its allegiance to Draco, and it wouldn't work as well for anyone but Draco.”
Dumbledore knew it meant Harry would need to die in order for Voldemort to truly die, so he was pleased to know that Voldemort's mistake in taking Harry's blood might just save Harry's life.
So when Ron said three, it wasn't a mistake. He meant there were three more horcruxes to destroy before being able to destroy the fourth and final piece which was in fact Voldemort himself.
No, Harry was not immortal. As the other answers said, the Horcrux protected Voldemort, not Harry.
This theory suggests that each time he created a new Horcrux, that specific Horcrux diminished a part of his soul. Thus, his nose began to sink in, eventually disappearing altogether. Due to his tampering with dark magic, his human appearance evolved into a more snake-like state.
Draco Malfoy's mother Narcissa was cold, cunning and devoted to the Dark Lord. But she was also a mother, which meant she was willing to risk everything to make sure her son was safe. When Harry survived Voldemort's Killing Curse for the second time, Narcissa pretended he was dead so she could get to Draco.
Though Harry encountered many opportunities that deemed Avada Kedavra necessary, it remains as one of the Unforgivable Curses Harry Potter never cast. For one, he viewed the spell as an immoral practice commonly used by users of the Dark Arts.
Neville's role in the prophecy in Order of the Phoenix is frequently referred to in a hypothetical scenario where Neville was the Chosen One rather than Harry. It is often suggested that Voldemort chose Harry over Neville because of Harry's half-blood status.
He truly believed the Elder Wand had to be passed down through murder, because that is what the legends say. But even if he knew that one only had to be disarmed, Voldemort was still too arrogant to do that. He kills anyone in his way.
Erroneously believing Snape is the master of the Elder Wand and that Snape's death will make him the master of the Wand, Voldemort kills Snape by having his pet snake Nagini bite him through the neck.
Severus Snape is one of the most divisive characters in the entire "Harry Potter" series. He was a double agent, so many character details were kept a secret. His mother was a witch and his father was a Muggle, leading to the moniker "The Half-Blood Prince."