This essay explores just why Voldemort's soul latched onto Harry and why it didn't latch onto anything else when his soul was ripped in half.
We all remember Dumbledore's explanation in Deathly Hallows during the scene in Snape's memories about Harry being the seventh horcrux that Voldemort never meant to make; That when he tried to kill Harry, the act was so violent and heinous that his soul ripped in two and latched onto the only living thing left in the house. But why Harry's soul?
We can't say that it was simply because Harry was the only living thing left in the house when Voldemort tried to kill him because earlier in the book Harry finds a letter from Lily to Sirius saying that Harry "nearly killed the cat" (Deathly Hallows page 180 US hardback) while riding around on the broom that Sirius gave him for his first birthday. So if the cat was there, why didn't Voldemort's soul latch onto him or her?
We could assume that the cat died in the three month time span between Harry's birthday and Halloween. But that would be too easy. Let's assume that the cat was still alive when Voldemort tried to kill Harry. Maybe the cat didn't have a soul, but after looking at Mrs. Norris and Crookshanks' behavior I don't think that JK Rowling would necessarily say that no cat, or animal for that matter, was without a soul. So if the cat had an available soul to reside in, why didn't Voldemort's soul go to it instead?
Maybe Voldemort's soul went into the nearest living thing. That's another explanation. But I don't think it satisfies this question completely.
Voldemort never said the incantation that was required to make a horcrux. In the sixth book, Harry watches a memory where Horace Slughorn tells young Tom Riddle how to create a horcrux, saying that there is an incantation you must say after having murdered someone. Possibly because the killing curse was directed at Harry, Voldemort's soul automatically went to him.
But, looking back at all of the other horcruxes, every single one of them has been something that was important to Voldemort. His family ring, the founders' belongings, his diary, and his snake were all extremely important to him and had value. Harry had value to him as well. Harry was the only thing that stood in his way to "greatness" and ultimate power over Muggles and the entire Wizarding World. So it is much safer to assume that because Harry was so important to Voldemort, it was the reason why Voldemort's soul latched onto him when he tried to kill him and his soul split into two.