Your question operates on quite a few false assumptions and a seemingly confused understanding of the Potter lore, which are well worth clarifying. I've broken it down into 3 main problems with your question which I will attempt to iron out:
- Horcruxes do not bring you back to life
- Harry is technically not a horcrux
- The diary was not resurrecting Tom
"A Horcrux is the word used for an object in which a person has concealed part of their soul... Well, you split your soul, you see, and hide part of it in an object outside the body. Then, even if one's body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged."
—Horace Slughorn, Harry Potter and the Half-Blood Prince, Novel by J.K Rowling
1. Horcruxes do not bring you back to life
Horcruxes do not bring you back to life, despite what the events with the diary, in Harry Potter and the Chamber of Secrets, might lead you to believe (see below for more detail on the diary).
Horcruxes serve as containers for part of one's soul, such that if one's body is damaged or destroyed, they cannot die. They keep you alive/immortal when you would otherwise die, but they do not bring you back to life, since you cannot die in the first place.
When Voldemort unintentionally "killed" himself with the rebounding Killing Curse in Godric's Hollow, his body was destroyed but he did not die.
"You all know that on the night I lost my powers and my body, I tried to kill him."
".... I was ripped from my body, I was less than spirit, less than the meanest ghost. . . but still, I was alive. What I was, even I do not know... "
"...Nevertheless, I was as powerless as the weakest creature alive, and without the means to help myself...for I had no body, and every spell that might have helped me required the use of a wand. . . ."
... "Only one power remained to me. I could possess the bodies of others."
– Lord Voldemort, Harry Potter and the Goblet of Fire, Chapter 33, Novel by J. K. Rowling
Though his body was destroyed, Voldemort never died, thanks to his horcruxes. As a sentient pseudo-spirit (ghost-like weakened state), with the power of possession, he was able to, for example, mutate and share Quirrell's body, and later on, with the help of Wormtail, he is able to use a Rudimentary Body Potion to sustain his non-corporeal form in a deformed, rudimentary body, before later on using a ritual to restore his proper physical form, and full magical power, thus returning as he was nearly fourteen years prior, but not technically being brought back to life.
2. Harry is technically not a horcrux
Harry is technically not a horcrux, in fact he is referred to as a "temporary horcrux" or a "pseudo-horcrux".
Here is an excerpt from an interview in which Rowling herself explicitly clarifies Harry's status as a horcrux, including an impromptu definition of a horcrux
MA: After we got back from Carnegie Hall, we brought back your message of “Harry is kind of not really a Horcrux.” (SU: Oh, yeah.) And I don’t want to dwell too long on Horcruxes, but I’d love to hear you talking about how he is or isn’t, or wasn’t.
JKR: Well, I’ll tell you- do you know what? This will not end the discussion. (MA:Yeah.) (laughs) I know that, and you know that, but here is the thing: for convenience, I had Dumbledore say to Harry, “You were the Horcrux he never meant to make,” but I think, by definition, a Horcrux has to be made intentionally. So because Voldemort never went through the grotesque process that I imagine creates a Horcrux with Harry, (SU: Mm-hm.) it was just that he had destabilized his soul so much that it split when he was hit by the backfiring curse. And so this part of it flies off, and attaches to the only living thing in the room. A part of it flees in the very-close-to-death limbo state that Voldemort then goes on and exists in. I suppose it’s very close to being a Horcrux, but Harry did not become an evil object. He didn’t have curses upon him that the other Horcruxes had. He himself was not contaminated by carrying this bit of parasitic soul. The only time he ever felt it stirring and moving was in Order of the Phoenix, when he himself goes through a very dark time. And there’s a moment where he’s looking at Dumbledore, and he feels something rear like a snake inside him, and of course, at those times, it’s because the piece of soul inside him is feeding off his emotions. He’s going through a dark time, and that piece of soul is enjoying it, and making its presence felt, but he doesn’t know what he’s feeling, of course. Also, I always imagine that the Sorting Hat detected the presence of that piece of soul (JN: Yeah!) when Harry first tried it on, because it’s strongly tempted to put him in Slytherin. So that’s how I see it. (JN: Wow.) Now, I know that won’t end the debate, but I do think that the strict definition of “Horcrux,” once I write the Scottish Book, will have to be given, (SU: Yeah.) (JN: Yes.) and that the definition will be that a receptacle is prepared by Dark Magic to become the receptacle of a fragmented piece of soul, and that that piece of soul was deliberately detached from the master soul to act as a future safeguard, or anchor, to life, and a safeguard against death.
Aside from the author's word on the subject, you should also not forget that creating a horcrux requires a specific spell, which would of course require intention and preparation, which did not occur in the case of Voldemort, that night at Godric's Hollow.
"But how do you do it?"
"By an act of evil — the supreme act of evil. By commiting murder. Killing rips the soul apart. The wizard intent upon creating a Horcrux would use the damage to his advantage: He would encase the torn portion —"
"Encase? But how — ?"
"There is a spell, do not ask me, I don't know!" said Slughorn shaking his head like an old elephant bothered by mosquitoes. " Do I look as though I have tried it — do I look like a killer?"
—Tom Riddle and Horace Slughorn, Harry Potter and the Half-Blood Prince, Novel by J.K Rowling
We know that the reason why part of his soul latched on to Harry was because his soul had become so unstable, and this part latched on to the nearest living thing.
So, for the purposes of convenience in plot, Harry acted as a host for one of the eight parts of Voldemort's soul (six objects including Nagini + Harry + Voldemort himself (he always regarded himself as the seventh part: "Voldemort intended to split his soul into seven pieces, with six Horcruxes housing one fragment each and his main body the seventh.")), so you could say that insofar as he functionally acts the role of a Horcrux, without actually being one, he is a pseudo-Horcrux.
3. The diary was not resurrecting Tom
The diary was not resurrecting Tom when it was feeding on Ginny Weasley's life, instead it was strengthening itself, improving its abilities to act independently in the physical world, gaining the ability to actually manifest itself in semi-corporeal form by the time Harry confronts him.
See, Horcruxes have abilities and powers, including the ability to influence the physical world and possess minds. We know this from Ron's experience with Salazar Slytherin's locket, though it is most extreme in the case of Ginny Weasley, where she willingly embraced the diary's influence.
Had the diary's manifestation of Tom Riddle succeeded, it would just have meant that this horcrux would have been very powerful indeed, but there is no evidence to suggest that the power of a horcrux serves it in any way other than its original purpose, which is to protect its creator from death, not to facilitate a way to incarnate a new version of themselves (that wouldn't be far off from cloning oneself). It would have been one of the horcruxes with the most powerful self-defense mechanisms, absolutely (it could be argued that it already was, given that it was possessing a child to command a basilisk in Hogwarts), but there is no reason to believe that it would have lead, eventually, to a reincarnation or resurrection of Lord Voldemort himself. Remember that the purpose of a horcrux is to save its creator from death, not to be an avenue for reincarnation.
Conclusion: Horcruxes are not for resurrection, they are for protecting one from dying when their body is damaged or destroyed.