Dumbledore wasn't lying about what he saw in the mirror of Erised

Yes, though obscure our dear Dumblydorr's statements are, this one was actually true. He actually saw himself holding a pair of socks in The Mirror of Erised, but there's more to it.

Though one may not have realised this, hand-knitted items are invaluable treasures in the wizarding world. They're knitted without magic and full of love. Molly Weasley uses them as tokens of acceptance (and therefore refuses to 'waste' one on Fleur). 

Now let's imagine a teen Dumbledore sitting in a chair, and his sister Ariana approaches him holding a pair of hand-knitted socks for him. It is likely that Dumbledore refused, perceiving them as trinkets from an unwanted squib of a sister, as he believed in magical supremacy. What pain Dumbledore must have felt after looking back years later, having lost his sister, one can't put down in words. 

To the people who think that the scenario with the teen Dumbledore is a bit 'feeble', I think considering that Ariana struggled with magic and was never let out of her house (kinda like you and me nowadays), she must have picked up some small hobbies or skills here and there, and it is possible one of them was knitting. After all that explanation, I think that Dumbledore must have seen himself holding a pair of socks hand-knitted, with his sister Ariana in The Mirror of Erised.

Fun Fact: 'Erised' is 'desire' spelled backwards.

Also, gold star⭐if you got the 'Dumblydorr' joke. You're a true Potterhead