I have read a lot about Common Core and I support it. I think it is a valuable reform and something we should embrace. I have been exposed to the agreements against it and think some of the criticism may have merit, but on balance I think the pluses outweigh the negatives. Some of the arguments against it are very weak. Some verge on conspiracy theory stuff.
One of the arguments used against it, is that it is just too hard. School should be fun. Children shouldn't experience anxiety over school work. When I was a child, I stressed over spelling test and learning multiplication tables and there was no common core. Learning can't be all fun. Sometimes children do cry when they can't figure out how to do their homework. Maybe they need to be taught how to better deal with frustration. Sometimes leaning new skills is difficult.
One of the repeated criticisms about Common Core is that it requires abstract thinking and reasoning. It seems the critics would prefer rote memorization. It seems they do not want children leaning to reason. The critics really do not like "word" math problems. In the link below to a video critical of Common Core you will see examples of what the critics think is wrong with it. Here is math question the video features: A box of crayons has 131 crayons and a bag of crayons has 128. Which has more crayons, the box or the bag? Now, what is wrong with that? Are American kids too dumb to figure out that 131 is greater than 128?
The video: Faces of Common Core.