11. Dumbledore Didn't Lie About What He Saw In The Mirror Of Erised
Albus Dumbledore is one of the most unreliable heroic figures in story-telling history, by design. He's liberal with the truth, his intentions and his past because he's playing a long-game designed to save the world from its most grave threat. To that end, he tells some lies, not only to remains mysterious but also to protect Harry and his other charges.
The strangest one he tells always seemed to be when he told Harry that all he saw in the Mirror Or Erised was a nice pair of wool socks. It appeared an enigmatic fib, designed to protect something even potentially ominous, because there could be no way someone as complex as the headmaster could have such simple designs. The solution to that conundrum was never actually offered, but in hindsight, if you read between the lines, what Albus saw was probably what he saw in the past too - Gellert Grindelwald.
Even more fitting than that explanation is the theory that Dumbledore didn't lie at all. Hand-knitted items are presented in Harry Potter's world as true treasures, because they are tokens of love where money isn't necessarily available. They're also knitted without magic and used by Molly Weasley to signify acceptance (she refuses to "waste one" on Fleur), so it's not too much of a stretch to imagine that Dumbledore might himself have been given knitted gifts from his sister Ariana, who struggled with magic.
Now imagine that he rejected those gifts as silly trinkets from a sister he wished he didn't have because of his beliefs in magical supremacy. Imagine he threw them away in disgust.
Perhaps Dumbledore's eventual deep regrets at what happened to Ariana and his embarrassment at her condition led his greatest desire to be to have her around to give him something as simple as a pair of socks she'd knitted.