The Sorting Hat determines what the inner qualities of each student are and then decides the Hogwarts House they will go into. Why does this need to be done, though? I titled this question this way for a reason. I'm not asking why they are divided into houses because that makes sense and it's normal (not necessarily into Houses, but into different groups for administration purposes).

Why is there a system in place that determines the qualities of a person and then divides them as if human characteristics can never change? The Sorting Hat seems to be the starting point for a messed up magical world.

Adam V has already mentioned the four founders wanting to have a way to select students who were eponymous with each founder's desired traits and skills in their students. If I'm to take your question literally, though -- why is the object used to sort the Hogwarts students a hat, instead of, say, a magical ruff, a pair of shoes, or a cravat? -- then I can offer this information from J.K. Rowling:

J.K. Rowling: The Sorting Hat does not appear in my earliest plans for Hogwarts. I debated several different methods for sorting students (because I knew from early on that there would be four houses, all with very different qualities). The first was an elaborate, Heath Robinson-ish machine that did all kinds of magical things before reaching a decision, but I did not like it: it felt at once too complicated, and too easy. Next I placed four statues of the four founders in the Entrance Hall, which came alive and selected students from the throng in front of them while the school watched. This was better, but still not quite right. Finally, I wrote a list of the ways in which people can be chosen: eeny meeny miny mo, short straws, chosen by team captains, names out of a hat - names out of a talking hat - putting on a hat - the Sorting Hat. POTTERMORE LINK - THE SORTING HAT - BOOK 1, CHAPTER 7 or SCREENSHOT.

Also, according to J.K. Rowling, the Sorting Hat is a Legilimens (screenshot); however, it does not possess human emotions per se. Were a human to be the one to sort the students, he/she might harbor subconscious prejudices that could lead to an incorrect sorting. The Sorting Hat is not human; it does not necessarily think like a human. It is the closest, I think, Hogwarts can get to a truly neutral party for sorting.

The exception to the "no emotions" rule, I think, can be found in Order of the Phoenix:

Have the houses been united

As they once were meant to be.

And now the Sorting Hat is here

And you all know the score:

I sort you into houses

Because that is what I’m for,

But this year I’ll go further,

Listen closely to my song:

Though condemned I am to split you

Still I worry that it’s wrong,

Though I must fulfil my duty

And must quarter every year

Still I wonder whether Sorting

May not bring the end I fear.

Oh, know the perils, read the signs,

The warning history shows,

For our Hogwarts is in danger

From external, deadly foes

And we must unite inside her

Or we’ll crumble from within

I have told you, I have warned you ...

Let the Sorting now begin.

Order of the Phoenix - pages 186-187 - Bloomsbury - chapter 11, The Sorting Hat's New Song

Based on the song that the Sorting Hat itself sang one of the years, it seemed that in the beginning, each of the founding wizards had their own preference on who to accept (except Helga Hufflepuff, who would accept any witch or wizard who wanted to learn).

Excerpt: (from Harry Potter Wikia)

Said Slytherin, "We'll teach just those

Whose ancestry's purest."

Said Ravenclaw, "We'll teach those whose

Intelligence is surest."

Said Gryffindor, "We'll teach all those

With brave deeds to their name."

Said Hufflepuff, "I'll teach the lot

And treat them just the same."

The hat also recognized the inherent error in dividing the students:

And now the Sorting Hat is here

and you all know the score:

I sort you into Houses

because that is what I'm for.

But this year I'll go further,

listen closely to my song:

though condemned I am to split you

still I worry that it's wrong,

Though I must fulfill my duty

and must quarter every year

still I wonder whether sorting

may not bring the end I fear.

Why is there a system in place that determines the qualities of a
person and then divides them as if human characteristics can never
change?

Curiously, the human characteristics evolve due to the environment you grow in. The sorting hat seems to just choose the "best bet" for the house you're most likely going to develop more comfortably.

So I'd say that the point of the sorting hat is to send you to the best possible house for you at the given moment. If in the future you happen to change your mentality, you're probably mature enough to accept it anyway - if you think about it, there really is no much difference to be in a house or the other. It isn't like you're unable to socialize with your Gryffindor fellas while you're a Ravenclaw...

Really old question. But as a professor with a PhD in personality psychology, I want to answer the underlying meaning behind your question rather than your question itself.

At least secondarily, what you seemed to be asking was: wouldn't the sorting procedure engender negative consequences for students?

The answer, I believe, is yes.

Firstly, it serves as a self-fulfilling prophecy. See, for example, the famous work of Robert Rosenthal on the Pygmalion Effect. To summarize, a psychologist gives a completely fake test to a number of children, and makes up results, which he gives the teachers. A small portion, he tells them, will "bloom" intellectually that year. At the end of the year, when he returns, those kids have indeed performed better than the other children, because (the author's interpretation) the teachers have responsed to those children differently (e.g., answering their questions with more alacrity, giving them more material because it is believed they can "handle" it). In other words, having the Sorting Hat say in front of a crowd of people (essentially), "You're brave!" or "You're smart!" or "You're basically evil!" will cause a) the child themselves, b) their peers, and c) the professors/staff to treat them as if they were those things. Through a number of subtle but persistent habits, behaviors, and attitudes, these things will therefore be more likely to actually come to pass, even if the child were not necessarily inclined in that direction. See also The Stanford Prison Experiment, which demonstrates that people tend to take on the roles assigned to them by others.

This is roughly akin to the socioeconomic concerns that educational psychologists have about testing that places different ethnicities into consequential programs (e.g., "gifted," "special needs").

Also, as you mention, it does not allow for the possibility of personality change over time. While people's personalities are generally consistent over time and across situations, and some researchers have believed that it stabilize in one's 20s or 30s, research is demonstrating that people's dispositions are actually dynamic across the lifespan. Thus, the Sorting Hat makes a guess about a person based upon a very preliminary sort of understanding of their traits at 11 years old, and pigeonholes them eternally, reinforcing its (potentially flawed or at least underdeveloped) estimate because of the fulfilling prophecy described above.

Finally, I want to point out that the Sorting Hat uses as it's personality assessement system one which current personality psychologists like the least: a categorical measurement. That is, you're either Gryffindor OR you're Slytherin OR... This is akin to saying that people are either funny OR they're not funny. Today, we a) favor a continuum when measuring traits (such as the Big Five), so that you can be "a little" funny or "moderately" funny, rather than FUNNY = YES or FUNNY = NO. Also we b) like to acknowledge the interaction between person and situation, such that in certain circumstances you might be funny (or brave, or loyal, or ambitious) whereas in other circumstances the same person might be a coward, disloyal, or passive. People are a lot more complex than the Sorting Hat gives them credit for.

So, my answer to your meta-question, or secondary question is, yes: the Sorting Hat is basically an evil social experiment. =) At least, in a real-world, developmental sense. That doesn't stop me from enjoying its role in the fantasy world from whence it comes.

It was to give each Founder’s House their preferred students.

The Sorting Hat himself explained that the four Founders of Hogwarts had different preferences in the type of students they wanted to accept, so the Sorting Hat was enchanted by them to decide which Founder’s House each student would be most compatible with, and assign students so the Founders would each have the ones they’d prefer in their House.

“Thus Hogwarts School began.

Now each of these four founders

Formed their own house, for each

Did value different virtues

In the ones they had to teach.

By Gryffindor, the bravest were

Prized far beyond the rest;

For Ravenclaw, the cleverest

Would always be the best;

For Hufflepuff, hard workers were

Most worthy of admission;

And power-hungry Slytherin

Loved those of great ambition.

The Sorting Hat’s song then goes on to say originally the founders wanted to have a way to have their favorite types of students in their Houses, even when they were dead and would have no part in the decision.

While still alive they did divide

Their favourites from the throng,

Yet how to pick the worthy ones

When they were dead and gone?

’Twas Gryffindor who found the way,

He whipped me off his head

The founders put some brains in me

So I could choose instead!”
_{^{- Harry Potter and the Goblet of Fire, Chapter 12 (The Triwizard Tournament)}}

The reason that the founders chose to determine the Sorting by their was quite simply because that’s how they wanted the students in their House to be chosen. They likely did know that people’s characteristics could change, but they needed to determine which Houses the students would be placed in, which would need to be done when they start attending Hogwarts, since it also decided what room the students would sleep in. Presumably, whoever took over running the school chose to continue the tradition in honor of the school’s Founders, so used the Sorting Hat like the founders had intended, and as years went by, it became an ingrained part of Hogwarts which no one really wanted to take away.