The curriculum shows different ways to do things, but for the most part, they really do want the kids to know the theory behind it, which tends to confuse kids without "math brains". They really want everyone to be on the same page. And they figure that if all the teachers were teaching all the same lessons, all over the nation, that we could have scaled results that would converge to one great national educational strategy. It's not a bad idea, but if your kids aren't moving fast enough, the curriculum really doesn't allow for teachers to stop and remediate. So with an external force driving the pace of the classroom, instead of it being led by student progress and understanding, it leaves a lot of kids with cognitive issues in the dust.
Why did they do it this way? The most altruistic reasoning would be to make sure that we, as a nation, have a national education strategy and we are all on the same page regardless of whether we are in California or Florida, New Jersey or Ohio. The most cynical answer is because these curriculum writers, educational materials makers, and educational testing materials makers wanted to sell more stuff but it's easier if the entire nation is standardized, so they don't have to put out 50 different sets of materials. I think the answer is somewhere in between. I think this was done to try to catch students up from poorly performing states, and with our meritocracy being what it is, test makers are making a lot of money, especially if they only need to produce one version of everything.
I think that while it's a great goal to aim for, my 11 year old has trouble reading and doing simple math equations, and we are finally at the point educationally where we are allowed to step him down to a remedial class that does not have the common core schedule attached to it. He was unable to keep up with that schedule as were a lot of the kids in his class. The teacher resorts to reading books out loud to the kids because none of the kids are good enough readers to read through the passage in the time that common core gives. While the teachers are able to change some of the materials to reflect the student's current achievement level, they cannot change the standards which are very specific--e.g. Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context. So if a student is unable to understand similes, it's hard for them to explain them, etc. The classes move too fast, because they are required to keep up with the neurotypical students, but these kids need more time and need it presented more simply. The teacher is very limited in what she can change and she cannot change the pace of the class. It does not allow for any flexibility in teaching, which isn't good for non typical students.