Duas razões relacionadas.
Ele não sabe o que realmente é
Sirius é vago quando dá o espelho para Harry, e fica claro que Harry nunca abre o pacote até que seja tarde demais:
'I want you to take this,' [Sirius] said quietly, thrusting a badly wrapped package roughly the size of a paperback book into Harry's hands.
'What is it?' Harry asked.
'A way of letting me know if Snape's giving you a hard time. No, don't open it in here!' said Sirius, with a wary look at Mrs. Weasley, who was trying to persuade the twins to wear hand-knitted mittens. 'I doubt Molly would approve - but I want you to use it if you need me, all right?'
'OK,' said Harry, stowing the package away in the inside pocket of his jacket, but he knew he would never use whatever it was.
Harry Potter and the Order of the Phoenix Chapter 24: "Occlumency"
Tanto quanto Harry sabe, é uma espécie de farol de emergência; ele não sabe que é um meio geral de comunicação, e ele não se importa em saber.
Ele tinha esquecido disso.
O contexto em que Harry descobre o que Sirius deu a ele deixa claro que ele não costuma pensar sobre o presente:
Harry pulled some crumpled robes out of the very bottom of his trunk to make way for folded ones and, as he did so, noticed a badly wrapped package lying in a corner of it. He could not think what it was doing there. He bent down, pulled it out from underneath his trainers and examined it.
He realized what it was within seconds. Sirius had given it to him just inside the front door of number twelve Grimmauld Place.
Harry Potter and the Order of the Phoenix Chapter 38: "The Second War Begins"
Harry está passando por uma fase difícil por meio do OotP , e especialmente nas horas que antecederam a necessidade de contatar o Sirius. É perfeitamente compreensível que esse pacote despretensioso, que ele explicitamente disse a si mesmo para não usar, tenha deslizado sua mente.
A Coisa dos Olhos Azuis
Para corrigir seu equívoco, Harry não vê nada quando tenta usar o espelho, exceto por seu próprio reflexo:
[Harry] looked around to make sure there was nobody else there; the dormitory was quite empty. He looked back at the mirror, raised it in front of his face with trembling hands and said, loudly and clearly, 'Sirius.'
His breath misted the surface of the glass. He held the mirror even closer, excitement flooding through him, but the eyes blinking back at him through the fog were definitely his own.
He wiped the mirror clear again and said, so that every syllable rang clearly through the room:
'Sirius Black!'
Nothing happened. The frustrated face looking back out of the mirror was still, definitely, his own.
Harry Potter and the Order of the Phoenix Chapter 38: "The Second War Begins"
Os olhos azuis que você se lembra de ver podem ser uma referência ao filme, já que Daniel Radcliffe (in) tem olhos azuis, mas também pode ser uma referência a Relíquias da Morte , quando Harry observa periodicamente em um caco do espelho e ocasionalmente vê Aberforth Dumbledore olhando para ele.