Harry Potter uses the resurrection stone to bring back four of his loved ones from the dead, but why didn't he also resurrect Dumbledore?
Harry Potter brought back four of his loved ones with the resurrection stone in Harry Potter and the Deathly Hallows, but surprisingly didn’t revive the newly-deceased Dumbledore, and here’s why. After Dumbledore died at the end of Harry Potter and the Half-Blood Prince, he gifted Harry two items in his will: The sword of Godric Gryffindor and the golden snitch from the first Harry Potter film. While he wasn’t able to receive the sword, he was given the snitch with a coded inscription that said “I open at the close.” Harry later realized this was meant to be used before he sacrificed himself to Voldemort, with the golden snitch enclosing the resurrection stone that would revive his loved ones from the dead to help guide him into death.
When Harry finally used the resurrection stone in the woods, he brought back to life his mom, dad, godfather Sirius, and mentor/family friend Lupin. As Harry prepared to die at the hands of Voldemort for the greater good, his deceased loved ones eased his fears about death and comforted him until the moment Tom Riddle used the Avada Kedavra curse on him. Considering Dumbledore was one of the most important figures in Harry’s growth at Hogwarts, it surprised many that Harry Potter's protagonist didn’t also resurrect the influential headmaster who had just recently died.
Dumbledore was a constant presence in Harry’s life, but, by the end of Deathly Hallows, Harry chose to bring back the four people he had the closest connection to who would soothingly bring him into his own death – his mother, father, godfather, and mentor figure. Harry’s close relationship with Dumbledore reflected a teacher-student dynamic in which the wise wizard guided Harry with his magic and inevitable path in destroying Voldemort. Dumbledore was important to Harry’s growth, but there wasn’t real love between them in their relationship, unlike Lily and James Potter, Sirius, and Lupin. These four figures were the only family he truly knew, so he wanted them to comfort him into death. Dumbledore wouldn’t have granted this same unconditional love to conclude his life; he was simply looking out for the greater good and fulfillment of the prophecy in his relationship with Harry.
Harry had also just seen the memories of Severus Snape in the Pensieve right before he went into the woods with the resurrection stone in Deathly Hallows. These memories showed Harry that Dumbledore hadn’t truly cared about the wellbeing of Harry as a human being - much less a child - and was “raising him like a pig for slaughter.”While Dumbledore would still be a wise figure to Harry in teaching him the importance of sacrifice for the greater good, the Hogwarts headmaster was not a comforting character with unconditional love that Harry would want at his side as he died.
Rather, as an insightful adviser, Harry had Dumbledore waiting for him in Limbo where he could choose to live or die after being “killed” by Voldemort. Meeting him in King’s Cross Station, Harry needed the advice of Michael Gambon's Dumbledore (whether in his head or not) to objectively convince him why he should live. Dumbledore rarely acted on emotion and made decisions based on logic and benefit to the greater good, so he was the figure that needed to help Harry decide whether to keep living and destroy Voldemort, or move on to death and be with his family. He wanted Dumbledore’s wisdom as he decided his next move in life or death, but needed his loved ones and family as he prepared to sacrifice himself in Harry Potter and the Deathly Hallows.