Author's Note: Inspired by reading Publicola's Wait, What? (very much like this fic, but much more fleshed-out) and commenting on Dumbledore's reasoning regarding the Horcrux.
Then I realized matters were even more... awkward... then their interpretation.
Note for unusually emotional!Harry, but, in fairness, he is twelve here, and the knowledge is uniquely horrifying.
"You can speak Parseltongue, Harry," said Dumbledore calmly, "because Lord Voldemort — who is the last remaining descendant of Salazar Slytherin — can speak Parseltongue. Unless I'm much mistaken, he transferred some of his own powers to you the night he gave you that scar. Not something he intended to do, I'm sure…"
"Voldemort put a bit of himself in me?" Harry said, thunderstruck.
"It certainly seems so."
"Like - like he did in the diary?"
Dumbledore seemed to weigh his words for several seconds before he spoke. "I cannot be certain. It is difficult to determine. Especially in light of the protection your mother passed into you, which-"
"I've got a bit of Voldemort in me?" Harry repeated, hand going to his scar. More than ever, he wished he could obliterate the horrid thing, but now for far more serious reasons than unwanted attention. "Like the diary? It - Could it come out and possess me?"
Dumbledore continued to hedge about the subject. "I am not certain. The inadvertent nature, your mother's protection, your own will-"
"But you considered it might be a possibility?" Harry said in horror. It made sense, now, why Dumbledore had not intervened to reason with the students who thought he might be the Heir, had not reminded them all that his mother and one of his best friends alike were Muggle-born, had not pointed out he was hardly willing to ally himself with a cause that had claimed both his parents' lives...
In response, Dumbledore only pressed his fingertips together and looked towards the ceiling, seeming to regret saying too much.
"You thought I was being possessed," Harry said. "You thought I was the Heir - or the piece of Voldemort in me was. You thought it was me - You -"
"I could not be certain..." Dumbledore hedged again.
"But I was the only suspect, wasn't I?" Tears sprang to Harry's eyes; in horror and humiliation, he took his glasses off and mopped at them, but his horror at the unfolding truth was greater. "You thought it had to be me. Lockhart wasn't a host for Voldemort-" God knew Voldemort, whatever his evil, had too much dignity for that- "And you didn't know about the diary. And Voldemort was the only descendant of Slytherin. Who else could it have been?"
He couldn't make out Dumbledore's face, with his glasses off, but the silence was ominous.
"Why didn't you lock me up?" Harry asked, broken-hearted that he had to ask, yet not seeing another option. "If you thought I was the Heir - or his vessel - why didn't you take steps to stop me?"
"Such extreme steps..."
"I - I know. B-but - it would have proved it wasn't me if the Heir attacked while I was kept under guard, wouldn't it? You - could have told everyone I was being kept safe. Or something. Come up with some excuse. Pretended not to believe it, but said you were doing it t-to satisfy p-public demand..." Harry took in a great gulp of air. "Am I a danger? A-Am I going to have Voldemort start growing out of my head?" He seized at the scar, kneading the thin flesh; if he could tear it out, he would. "I-Is that why my scar hurt whenever Quirrell was around? W-Was it trying to rip its way out of me a-and - and rejoin him?"
"I have said too much," Dumbledore said with a sigh. "There is no use in letting you know so soon, and much harm. Poor boy... why take away what scant childish innocence you have managed, against all odds, to preserve, and what little childhood you have left? There is no curing your condition, after all..."
Harry's blood turned to ice. "Sir?"
"No - I can see no fate before you but sorrow. Pardon me, Harry, but I am a fool. Allow me to delay it a little while longer. I have always been a coward, I'm afraid... If you but knew my brother, he would tell you how much..."
"I - I don't understand -"
Author's Note: Well, might as well keep Albus's characterization in line with his Order of the Phoenix speech.
In all seriousness, it makes too much sense that Albus thought the Heir-attacks were the result of Harry's Horcrux. Who else would it have been? "[N]o wizard had ever done more than tear his soul in two." One piece is accounted for - Quirrellmort/Albaniamort. The other piece would then be Harrymort. Either there's a new Heir who just happens to replicate Tom's modus operandi exactly, or Tom's returned. So did he hitchhike from Albania again, or did the contact with the other half of Voldemort at the end of last year awaken something... unsavory in Harry?
As for why he didn't take any precautions in response to his suspicion: Albus being Albus. He didn't take precautions beyond telling Snape to 'keep an eye on Quirrell' the prior year, despite an open assassination attempt. He didn't take serious precautions to contain Harry when his mind was being actively violated by Voldemort and, for all he knew, the Dark Lord might seize control of Harry and perform a kamikaze run on the school. He didn't take serious precautions to neutralize Draco when his assassination attempts kept going wide of the mark and nearly taking out innocents. Why would this year be any different?
Yes, Memory Charms are cliche. At least, for this year, they're on theme!