Let me start by saying that I think the Common Core is a "good thing". It establishes a set of standards against which students, schools, districts, states, and the nation can be measured. So why is it apparently controversial?
The major reason is that the critics confuse standards with curriculum (what is taught and how it is taught) and with assessment (what is measured). The Common Core is neither. Teachers, schools, districts, and states still define their own curriculum and they still define their own assessments. The commonality is that the standard is out there in front of them and is the same for all. The second big change is that the standard is a benchmark or milepost and not a destination.
The best analogy is that of the driving test. The state legislature or Department of Transport sets the standards which a driver needs to meet to obtain a licence. However, neither dictates what is taught and learned, how it is taught or learned or other than in general terms how it is assessed. The student and instructor decides how and when and where to teach and learn and to practice, and what is taught and learned. Get any of this wrong and the student may not meet the standard.
The Department of Motor Vehicles or the sheriff's office decides on what is then tested and on how. As any discussion of where (and when) a driving test is taken will show, tests vary considerably. I remember one test in one jurisdiction consisted of driving out of the parking-lot. At the corner (with a traffic-light), the assessor told me to go round the block and back to the office. End of test. I had met the standard. He told me leaving the parking-lot (an uphill exit with a tricky stop sign) tells him whether a driver is competent or needs a full test. Yet I also remember moving to another state, despite driving for a long time and although I wanted only to exchange licenses, having to undergo the entire beginning-to-drive test.
So the standard was set for the assessor who then decided how to measure whether the student met the standard.
A Common Core standard like "the student can count 1 - 100" allows the teacher, school, district etc to decide on how to teach this through activities, games, puzzles etc etc and separately to decide how to assess it. These curriculum and assessment decisions are not part of the Common Core. In the end, what matters is whether the student can or cannot count through 100.
Note that counting through 100 is not the same as stopping at 100 and the Common Core does not say "count through 100 and no more". The teacher, school, district etc can decide to go to 110 or 120 or even 1000. They can do what they want, but at some point their students must be assessed against the standard: no matter what else the student can do, can s/he count 1 - 100?
That is why I like the Common Core. I get to decide when, how and what to teach as long as at some defined time, my students can all show that they meet the standard. I can mix and match standards, I can focus on standards where my students may be weak. I can focus on other standards which I think are important for my community. Above all, I know where my students are compared to all the other students in the US (and around the world actually) because I have shown they can count 1 - 100.