After reading the title to this question on Movies.SE, my initial reaction was that Harry DID use the resurrection stone, right before he gave himself up to Voldemort. My question is, why didn't he resurrect Dumbledore? Everyone who meant a lot to Harry in their/his lifetime was resurrected when he rubbed the stone, so why wasn't Dumbledore?
At this moment Harry was doubting whether Dumbledore really was the same person he thought he was
He was frustrated with all the cryptic clues Dumbledore left him, instead of telling him exactly what to do concerning the hallows and horcruxes, the Dumbledore he had idolized seemed to be completely different from what he was really like, based on what he heard about him from Rita Skeeter and Aunt Murial. Even his own brother confirmed that Dumbledore was the type of guy who would lie and cheat you to manipulate you into doing what he wants, and set you up to do tasks that you would surely fail in
Also, he was sure he wasn't going to come back out of the forest, based on what he had seen Dumbledore say in Prof. Snape's memory, and the fact that he really did believe Dumbledore might have wanted him to get killed at this point in time, "for the greater good".
Given these facts, I think it is more logical that he would want emotional support from his parents, Lupin and Sirius who fought and fell trying to save him, than someone who just thought of him as a disposable pawn in a bigger war.
I think this was because Dumbledore had done his job as a guide for Harry. Throughout the books, the trio grows up, and learns to rely more on themselves and less on teacher's advice, which includes Dumbledore's. This may be symbolic of Harry growing up. At this point Harry knows that Dumbledore had died peacefully, and that he very much wanted to die (and what Snape did was in fact mercy killing). Also, at this point there isn't much Harry could ask or learn from Dumbledore - after all, he is going to die himself.
On the other hand, Harry wanted very much to meet his parents since the first book, when he saw them in the Mirror o Erised. It's nothing rational, but simply a wish of child.
Lupin and Sirius were the closest thing he had to role models - Dumbledore was too distant for that (again, by design - he wanted Harry to become independent). Sirius was the closest thing Harry had to a family, blood-relation-wise. Lupin was also his friend (sort of), and someone he respected.
I think this scene is symbolic as Harry grows up to the same level as the people that he resurrected - in a sense, they all dies fighting for the greater good, in order to protect ones close to them.
To my mind, the answer is that he didn't mean so much to Harry, as you would think. All the resurrected were practically his family, and Dumbledore, well, just his teacher.