The reason I am discussing the implications of the soul being split versus it being merely torn is because others have argued that there is a separate spell to completely split the soul. I feel that it is an important enough distinction to make since Tom Riddle really became interested at that point - interrupting his professor to hound the point. I think it does have relevance in the Harry being a Horcrux discussion because it deals with the timing and intentionality of making a Horcrux.
And semantics always have a meaning in the story. It's valid to argue on the basis of semantics, wether people agree or not.
As far as Slughorn's knowledge of how Horcruxes are created, he is the only authority we really have on the subject aside from Dumbledore and Voldemort. As Voldemort has not discussed them at all and Dumbledore is more concerned at the moment on finding and destroying them; I treat Slughorn as an authority on them. Of course he's hesitant to discuss them; he's not supposed to tell Tom anything about them! Hence the modification of the memory.
More to your point of argument:
I don't believe, given that the world is magical, that the only explanation for the connection and similarities between Voldemort and Harry is for him to possess a piece of Voldemort's soul. Before, in Chamber of Secrets, Harry says "He put a bit of himself in me?" Dumbledore states "Unless I'm much mistaken, he transferred some of his own powers to you the night he gave you that scar. . ." I tend to think of it more like a blood tranfusion; the recipient receives part of the blood of a donor, complete with DNA - but the recipient does not become the donor in any way. Kind of a "magical transfusion."
I'll touch a tad bit more on this with this next bit, too.
Several reasons why I don't believe Harry can be a Horcrux:
From Sorcerer's Stone
1.
QUOTE(p372; paperback)
...to have been loved so deeply, even though the person who loved us is gone, will give us some protection forever. It is in your very skin. Quirrell, full of hatred, greed, and ambition, sharing his soul with Voldemort, could not touch you for this reason. It was agony to touch a person marked by something so good.
This one seems to me to argue that Lily's blood protected Harry from any part of Voldemort touching Harry at the moment of her death; even someone sharing Voldemort's soul could not touch him. It makes sense to me that his soul, by itself, would not have been able to penetrate that magic either.
Sorcerer's Stone
2.
QUOTE(p.333; paperback)
"Unless I am 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. . . ."
"Voldemrot put a bit of himself in me?" Harry said, thunderstruck.
"It certainly seems so."
From Order of the Phoenix
3.
QUOTE(p826-7; hardcover)
"I guessed, fifteen years ago," said Dumbledore, "when I saw the scar upon your forehead, what it might mean. I guessed that it might be the sign of a connection forged between you and Voldemort . . . For it became apparent, shortly after you rejoined the magical world, that I was correct, and that your scar was giving you warnings when Voldemort was close to you, or else feeling powerful emotion . . ."
Dumbledore, in several instanced (2, 3, 4, 5,) mentions that the scar links Harry to Voldemort by a special magical connection; and also explains the transference of power; but he never has alluded to it being a piece of Voldemort's soul - which I think would have been pretty important for Harry to realize while Dumbledore was teaching him about the implications of Voldemort's Horcruxes.
4.
QUOTE(p842; hardcover)
He gave you that scar that has proved both blessing and curse. . .He saw himself in you before he had ever seen you, and in marking you with that scar, he did not kill you, as he intended, but gave you powers, and a future, which have fitted you to escape him not once, but four times so far -- something that neither your parents, nor Neville's parents ever achieved.
5.
QUOTE(p843; hardcover)
Consequently, he could not warn his master that to attack you would be to risk transferring power to you -- again marking you as his equal.
From Half Blood Prince
6.
QUOTE(p501; paperbak)
. . .in other words, the fragment of soul concealed inside it was kept safe and had undoubtedly played its part in preventing the death of its owner. But there could be no doubt that Riddle really wanted that diary read, wanted the piece of his soul to inhabit or possess somebody else, so that Slytherin's monster would be unleashed again.
Here we note (and in the description Ginny gives which I am not quoting) that the soul piece can possess a person and the possessed person is aware of the possession. Harry displays none of this.
7.
QUOTE(p503; paperback)
That seventh part of his soul, however maimed, resides inside his regenerated body. That was the part of him that lived a spectral existence for so many years during his exile; without that, he has no self at all. That seventh piece of soul will be the last that anybody wishing to kill Voldemort must attack -- the piece that lives in his body.
Here we see that all soul pieces must be destroyed PRIOR to going after Voldemort himself. Not something Harry could possibly hope to do if he has a bit of Voldemort's soul in him. Even if he thought to die at the same time, the risk is too great that Harry would die a half-second before Voldemort thus rendering Harry's death useless in the defeat of Voldemort.
8.
QUOTE(p507; paperback)
[speaking about Nagini]. . . and he seems to have an unusual amount of control over her, even for a Parselmouth.
Noting the control that Voldemort has over Nagini; which is not the same as the connection he shared with Harry creating a false-reality for Harry to get him to the Department of Mystery.
9.
QUOTE(p507; paperback)
A very interesting question, Harry. I believe not. I believe that Voldemort is now so immersed in evil, and these crucial parts of himself have been so detached for so long, he does not feel as we do. Perhaps, at the point of death, he might be aware of his loss . . .
This one strikes me as important, but I can't for the life of me remember what about it I was going to say! Gah, brain! Accio, brain!! I think it was along the lines of Voldemort not needing a Horcrux or a bond with a Horcrux in order to use and manipulate people or possess them. He just figured he could do it. That's not quite what I wanted to say, but until my brain comes back. . .
10.
QUOTE(p510; paperback)
. . .He heard the prophecy and he leapt into action, with the result that he not only handpicked the man most likely to finish him, he handed him uniquely deadly weapons!
Dumbledore saying that Voldemort handed Harry "uniquely deadly weapons" seems to speak against Harry being a Horcrux because it directly contradicts the evidence that a Horcrux would anchor Voldemort to life.
11.
QUOTE(p511; paperback)
But he knows it now. You have flitted into Lord Voldemort's mind without damage to yourself, but he cannot possess you without enduring mortal agony, as he discovered in the Ministry. I do not think he understands why, Harry, but then, he was in such a hurry to mutilate his own soul, he never paused to understand the imcomparable power of a soul that is untarnished and whole.
This mentions Harry's soul as being untarnished and whole. If he had a bit of Voldemort residing in him, Harry's soul would not have been so untarnished and whole. We've seen results of those used by Voldemort (Ginny, Nagini) to cause destruction . . . not something he could accomplish with Harry.
And a Note from JKR herself:
12.
QUOTE(The Interview from 2005)
MA: Here at the end you sort of get the feeling that we know what Harry’s setting out to do, but can this really be the entire throughline of the rest of the story?
JKR: It's not all of it. Obviously it's not all of it, but still, that is the way to kill Voldemort. That's not to say it won't be extremely an torturous and winding journey, but that's what he's got to do. Harry now knows — well he believe he knows – what he’s facing. Dumbledore's guesses are never very far wide of the mark. I don't want to give too much away here, but Dumbledore says, ‘There are four out there, you've got to get rid of four, and then you go for Voldemort.’ So that's where he is, and that's what he's got to do.
ES: It's a tall order.
JKR: It's a huge order. But Dumbledore has given him some pretty valuable clues and Harry, also, in the course of previous six books has amassed more knowledge than he realizes. That's all I am going to say.
If JKR says Dumbledore's never very far off the mark, and Dumbledore never alluded to or mentioned that Harry could possibly be one of the four remaining Horcruxes, then I think the chances are slim that he is one. When JKR and Dumbledore say Harry's got to get rid of the four and then go for Voldemort, then I believe that's what Harry has to do; and I think he'll be successful.
QUOTE(Albus)
. but as of right now.. the balance of the scale seems to be tipped heavily in favor of Harry being a Horcrux.
Just by looking at the text, I don't agree that the balance is tipped heavily in favor of Harry being a Horcrux.