At most schools an A is a 4.0, an A- is a 3.7, and so on. I feel like this system is not really representative of a person's true skill. For example, a person who got a 100% in a class will get the same GPA as a person who got a 94% in the class. However, a person who gets a 91% in a class will get a significantly higher GPA than someone who got an 89%. Why don't schools base GPA off the actual percentage that someone gets in a class instead of their letter grades?
The big reason: exact numerical scores are not comparable across classes and professors.
Suppose I told you that two students took a class offered in different semesters. We look at their transcript and see that student A scored a 94% with Professor X and Student B scored a 99% with Professor Y. Student B beat out the first person by five percentage points, but do we actually know that Student B is a better student? Maybe Professor Y is a soft grader or Professor X had a really harsh curve that semester. We don't really know whether Student B is better. All we really know is that both students did pretty well.
Hence, grades tend to be assigned and interpreted with a large degree of subjectivity, which fits the ABCDF model better than a score-based model. The general interpretation is:
A - excellent
B - good
C - average
D - needs improvement
F - failing
If the first and second student both get A's, then this means that an expert in their fields (the professors) have said that both students did excellent. This isn't a perfect system, but it is about as good a comparison as you can get.
At most schools an A is a 4.0, an A- is a 3.7, and so on.
This is true at most American colleges and universities, yes. (It's not true in most of the rest of the world, and the discrepancy is an issue when one wants to compare students from different countries, e.g. in graduate admissions.)
I feel like this system is not really representative of a person's true skill.
I have given out hundreds of grades in university courses, and I make no claim that a student's course grade is "really representative of their true skill." For instance, it has happened that I wrote grad school letters for an A- student and an A student for whom my primary interaction was teaching them the same course and that I wrote an overall stronger letter for the A- student: based on my interactions with him, I felt that his true skill was higher, whereas the A student did noticeably better on the midterm and the final (though both did very well).
For example, a person who got a 100% in a class will get the same GPA as a person who got a 94% in the class.
There seems to be a premise of this question that universities use standard "letter grade cutoffs." This is really not always true (though it is sometimes true, and it would be interesting to understand this better). These cutoffs have not been applied at any of the universities I've been affiliated with as a student or instructor: University of Chicago, Harvard, McGill, University of Georgia. (See e.g. Question 12 here.) To be honest -- and in part because my own experience with American universities, though quite temporally extensive, is far from universal and probably even from generic -- such talk reminds me of high school, and I get surprised when university students think too seriously about it. (And this sometimes includes my own university students!) In the STEM fields in particular, it is common for exams to be written in such a way that a 50% grade would be a clear A and a 90% grade would be preposterous.
Let me say though that I have not seen it go the other way: in any class I have ever taken or taught: yes, 94% is worth the same letter grade as 100%. One could go on at great length about this, but for now let me say: I see nothing inherently problematic here from anyone's perspective.
Rather I would like to call attention to the fact that there is a mistake above: students who get a 100% and a 94% will probably get the same course grade. GPA means grade point average. This error becomes more clear as follows:
However, a person who gets a 91% in a class will get a significantly higher GPA than someone who got an 89%.
No, this is really not the case. The typical American university student takes about 40 courses overall. So a student who gets A's in all but one course and fails the other course will have a GPA of (39*4 + 1*0)/40 = 39*4/40 = 3.9. If that student got at least a C+ instead of an F, their GPA rounded to one decimal place would be 4.0. In fact, my undergraduate GPA rounded to one decimal place was 4.0, though I remember well the course in which I received a B (the first graduate course I took) and more vaguely that I got less than A grades in at least two other courses. (Because culturally speaking a "4.0 GPA" generally implies all A's, I reported my GPA to two decimal places.)
This is, I think, a really key point: the inference of skill and achievement from course grades is a statistical process, and like most statistical processes, investing too much meaning in any one data point is dubious. I am currently directing graduate admission in the math department at UGA. There are occasions when individual course grades are meaningful to us: a student who has generally good grades but quite poor ones in two or three key courses that are the most foundational to graduate success is viewed negatively beyond the influence of the GPA (and this of course is why we do not just look at GPAs but get much more information, including full transcripts and lists of textbooks from the courses taken in the major). But for one of these key courses -- say real analysis -- what if one student gets a B+ and another gets an A-? Then we really don't care, and if we don't care, I'm not sure who would.
Let me finally make a few more remarks about the system of letter grades at universities.
There is nothing especially clever or apt about it. Another answer claims that we have the system basically due to historical inertia. The answer goes on to say some other things that I disagree with, but I certainly do agree with this. It is easy to pick apart the particulars of the system -- why no E? why no A+? [or if you do have an A+ -- as some universities do -- how do you figure that into the GPA?] Why pluses and minuses at all? (In fact, UGA had no plus/minus grades for many years, and the aforelinked FAQ is in fact an FAQ about the use of plus/minus grading!) Most importantly Why choose the same grading scale as is used in K-12 education, so that students will come to college/university with many preconceived notions about how grades will be assigned that they will gradually find out can be quite inaccurate?
A wider range of grades is not necessarily "better" or "more accurate." You hear a lot about grade inflation, and it is interesting that the language subtly conveys that it is somehow a problem. It is much more interesting to try to explain why it's a problem. One argument advanced along those lines is that it blurs distinctions between academic achievements. My colleague Jordan Ellenberg wrote a nice article demolishing this argument some years ago. The main idea is the one I gave above: students are taking a large number of courses. We could have just two possible grades, "excellent" and "very good," and as along as instructors assign the "very good" grade to students in a broad enough set of circumstances, over time the magic of probability and statistics will serve to separate the students. In fact I think I would prefer a grading scale that has fewer grades and that is not reminiscent of high school grading. For me a very natural scale would be one that has three grades: the lowest one is given to students who have not met (sufficiently many) clearly defined course objectives. It would roughly correspond to the "F" in the current system, but it should be given for failure to meet objectives, not for a numerical score in a certain range or for the bottom X% of the class. The top grade should be given to students who excelled in the course in some meaningful way (not for a numerical score in....). The middle grade should be given to everyone else. I think that such a system would lose little or no information from the present one, and more to the point, it is to a large degree how I think about letter grades as given.
I admit that it is entirely debatable, but I actually feel that it would be a net negative to record percentage grades in transcripts rather than to "discretize" as is currently done. If you're a young student, then maybe you're proud of your 98% and want it to be recognized as better than your colleague's 94%. But a context in which students are fighting over that 4% is not necessarily conducive to better learning. For me, this situation conveys strong memories of high school, in which our (weighted) percentage scores in each course were used to compute our class rank. This led to a cohort of students who were highly motivated to get the highest possible scores on every exam. I remember students studying for several more hours in order to make sure they had memorized 100% of the material instead of 97% of it. But this memory space was relatively short term: it would have to be vacated for the next course, if not the next exam. These bright young people could have used this time in more valuable ways, academically and otherwise. By the way, the grapes may be sour but perhaps not in the way you'd expect: I was the valedictorian (i.e, class rank 1) of my high school class. At the time I had the suspicion that this achievement was less significant than it was being made out to be. Looking back from the middle of an academic career I can now confirm this. University students are significantly more grade-conscious than is beneficial to them in any way, including academically. Blurring the distinction between 98% and 94% seems quite healthy.
For most of history, it would've been tedious to average all of a student's course grades weighted by credit hours. It was a lot easier to call an "A" a 4, a "B" a 3, etc., then just average.
It made curving a lot easier, too. Teachers could just sort the grades, then the top 10% got an A. Who wants to calculate an actual normal curve by hand? Heck, how many teachers even knew how to?
Today, cultural inertia
Today, it'd be a lot easier to do the calculation without all of the arbitrary rounding. We can do away with the arbitrary break point that's between 92.9% and 93.0%, and we can do away with how a 93% is the same thing as a 100%.
We don't need a simple method for curving because we've got computers and spreadsheets that'll calculate an actual bell curve, rather than the weird sorta-bell-curve that comes from splitting students up into discrete grade categories like A/B/C/D/F.
Today, we can do away with that common situation where students reason that getting a 75% on the final exam is the same thing as getting a 100%, leading them to not study or review the material.
But, suppose that an instructor or dean reads this question and agrees that the current system is messed up. What could they actually do about it? They're caught up in cultural inertia; same reason those of us in America still use inches/feet/yards/miles rather than meters with a metric prefix.