The first thing one ought to do is show why they've ruled out some of the other entirely logical candidates:
Harry or Voldemort: I'm only including this for anyone who missed JKR and her publishers verifying that neither of them are the HBP.
A New Character: There was no room for another new character in CoS, and we know that HBP was the original title for CoS for quite some time. We weren't meeting with various and sundry Order members yet, and as a significant part of the book revolved around the new DADA being, well, uncontrollablely and irredeemably Gilderoy Lockhart, that rules out the only space for an entire new character to be inserted.
Another Student: We know enough to know that some are half-bloods, but I would argue that we don't care enough about any of them for their identity to support the full weight of having the book named for them. Think of how much we already cared about Ginny before she was made the key to CoS; sure, it wasn't much, but she was a Weasley, the last and only girl at that. That carried a lot of weight - weight I don't think Seamus or Justin Finch-Fletchly could support. And seeing as we already know Neville's pure blood (or can reasonably assume so by the fact everyone in his family was shocked his magic wasn't developing when he was a child), that rules him out too.
Lupin: Not introduced until book three.
Hagrid: If anything else about Hagrid had been packed into book two, it would practically have to have been retitled "Rubeus Hagid and the Chamber of Secrets," (whereas Snape had remarkably little to do). He's already been the answer to a book's key question once, and it's not like Harry's relationship with him is so multi-facted it could support 608 pages (and that's the shortest version).
Remember: This probably won't be like Chamber of Secrets. An heir is one thing - we can assume that for quite a few generations there naturally would have been heirs to the house founders, so when something related to the school proved connected to one, it wasn't beyond the realm of expectation. But it's not like we've any reason to believe there are magics in the school that only half-blood male royalty can do.
Because of this, it's natural to assume it's Harry's relationship with the HBP that will be key to the book, not a quest to discover who it is.
Dumbledore: If Dumbledore's mother or father are still alive - a key requirement to being 'prince' and not 'king' - I'd be fall-down shocked, and not in that good Moody's-the-Death-Eater way. And even if that were the case (his brother is still alive, so you never know) there has not been a single sign that his relationship with them is so fascinating that it'll hold up the entire book, and that should prove to be one of, if not the, key plotline to the story. Whoever the prince is, we'll probably have a hundred questions relating to why he didn't make it common knowledge and/or isn't living like one.
Not to mention how much the wizarding world already has already delt with and talked about headmaster Dumbledore without anyone mentioning he's royalty.
So what rules in Snape's favor?
1. Ruling out students, Order members, and new characters (as I did above, whether you agree or not), that leaves staff. Of the staff, Harry's most interesting relationships are with Snape, Dumbledore, and McGonagall. McGonagall is a woman, and I doubt it's Dumbledore for the reasons stated above.
2. He has the bearing for it. Maybe that shouldn't be a clue to me, but it is. ("Because I knew Snape pretty well by then and he was not about to wear a turban." JK Rowling on the end of book one.)
3. He plays a significant role in every book but book two: In the first he's the suspected villain, in the third his backstory and hatred for Lupin and Black provide key plotpoints (a phrase which in this case means 'could have caused the deaths of fairly big characters)(/Snicket). In the fourth, his role as a former death-eater and spy is discovered (More backstory? Why, thank you, I'd love some!). And in five...
4. Five to me is the clincher, for two reasons. The first is that Ms. Rowling is explicit in stating that Harry feels he will never forgive Snape. Never. This sets up a richly dramatic dynamic between them going into book six. The other, more obvious, reason is that she seemed to go to rather a lot of trouble to show Harry and her readers large amounts of Snape's backstory. He is by far the non-trio character whose life we know the most about. There's so much information and effort expended in his backstory, I put it to you that he's the only character currently rich enough to have his relationship with Harry carry the book.
5. The adult UK book 6 cover: What, Miranda Goshawk was sold out that day? (Not a clue so much as a little instance of the fingerpost).
6. The Snape name was not mentioned in connection with the Black Family Tapestry of Inbreeding. This could mean that there's something about his heritage that had to be kept quiet for a while. True, Harry could have just not thought about it - but I suspect it'll be a cold day in muggle hell when Harry is confronted with information regarding Snape's family outside a traumatic Occlumency lesson and doesn't spare a sentence or two's worth of shock that the man didn't simply hatch fully grown from a Basilisk egg at midnight in a especially creepy graveyard.
7.
Bite me. This may be only a theory for now, but gratuitous mention of them has popped up enough for me to be suspicious. And if it turns out to be the case, it would certainly explain why there was a member of a kind of royalty somewhere in Britian that hadn't already been outed as such.
Remember, if it's a character we already know (see reasoning for that above) then there'd have to be
a very good reason why their status as royalty is being kept secret.
That's it. Those are my reasons. I may be wrong; I thought Hagrid was going to die in the last book and I once told a customer when asked what the books were about that they were "the story of a complcated potions master, as seen through the eyes of one of his students" (mind you, that was for very important reasons... that involved my having fun). But seeing the canon in a Snapecentric way is like seeing the world through rose-coloured glasses: your perspective may be warped but you tend not to mind the view!
P.S. If Snape's the HBP, then Al Roker is
the man: Roker: "How about Snape? Is Snape the Half-Blood Prince? What about Snape? Is it Snape? Tell me!" (Hits Arthur Levine with papers) "Tell me if it's Snape! How about Snape? I wanna know about Snape!"
Levine: "What is it with you and Snape?!"
Roker: "We go way back. Me and Snape have this thing... All right, thank you for coming, very nice meeting you..." (To audience) "Again, Harry Potter and the Half-Blood Prince... it could be Snape... hits shelves July 16h. We'll be back after these messages." (Suddenly lunges at Levine) "IS IT SNAPE?"