Ok, I've finally had a chance to read the article, and watch the video clip, all while taking notes. I'm guessing this post will be long, so please bear with me.
We'll address the video first, which has different points, or in a different order than the list in the article. If these overlap, they will be dealt with only once, and not repeated when I get to the list from the article.
Point 1: Ignores Parental Rights
This, at best, is ignorance. At worst, it's either outright lies, or teachers being dishonest. The public school system itself has long had a history of teaching what they will without parental input; but that's only because parents today take on a passive role in the education of their children. Parents who take an active role make changes. The only thing that common core dictates that parents cannot change is the minimum standards that children must be taught in order to be considered proficient (we're going to come back to the word, "minimum" later). It does not have it's own curriculum. As a secondary education college student (I'm a physics/math dual major with a sec. ed minor), I am being taught this over and over, that common core does not make teaching easier, and that I am still going to have to come up with my own lessons, my own lesson plans, and even decide which curriculum to use.
All this, parents can have a role in. It's only the passive ones who have no say.
Point 2: It Is Materialistic and Naturalistic
Even though they have a flawed premise, even what they use to reinforce this idea is flawed. Common core has as one of its goals to prepare students for college and/or the work force. This is obvious. But the goal of common core standards is critical thinking. As we will see in the next point, this is a good thing. While getting students ready for further education is a huge goal, the main goal is problem solving and critical thinking.
Point 3: It Dictates What Will Be Taught
And here they fall flat on their face. I can tell you firsthand that this is completely untrue. After all, as a secondary education student, I am learning about common core and how to design lesson plans and curriculum to fit the standards. Notice how I worded that. I am learning ... how to design lesson plans and curriculum. I, as the teacher, have to decide what curriculum to use (going back to point 1, parents can get involved here, but they usually don't). The only dictates of common core is the minimum standard that must be taught. If students go beyond that minimum, then they can and will.
Point 4: Uniformity Alone Does Not Improve Education
Can I start this out with a "duh"? This one's obvious. But it does not negate the role of uniformity in improving education. It's like saying, "I don't have to take math, because math alone will not teach me physics." No! But it's an integral part of it. If students are taught at a uniform standard, then moving schools or switching teachers does not hurt the child's education. And just for good measure, I'm going throw the sentence in here again: common core dictates a minimum standard.
Point 5: Skips Good Literature
I love how they say this, and then the very next sentence they say, "Public schools have always been against good literature." Hmmm.... sounds like they just defeated their own argument right there.
Point 6: Promotes Inferior Math Skills
At first glance, it seems they have scored major points here. After all, Professor James Milgram, a Stanford Professor who was involved in it's creation said that it actually had a lower standard than California's "pre-core" standards. But, on further inspection, we find that Professor Milgram's critique wasn't academic, and was not honest.
In his assessment, he listed 3 common core standards and compared them against California's previous standards. However, he left out the rest of the common core standards. A side-by-side reading of California's previous standards and the common core standards shows that they are identical. As a math professor, Professor Milgram should know that a number cannot be less than itself.
Point 7: Imposes a Cult of Testing
Ignoring their use of "cult" to evoke negative emotions and be sensationalistic, this again is in no way connected to common core. In fact, at my university, we are taught that testing to see if children are up to standard should be as nonintrusive as possible. In other words, students shouldn't even know they are being evaluated, unless it is an actual classroom test. Each lesson should have an evaluation, but it's not a test. And all this "high stakes" nonsense is just that: nonsense.
Point 8: It's Unpopular:
So is Jesus. Not enough? Well, how about the fact that most people are uninformed of what it actually is, and only see videos like this trash, instead of actually doing their won research into what it actually is?
Point 9: It Collects Massive Amounts of Data on Children
As with many points, this has nothing to do with common core. How could it? The databases were established in 2002, and common core wasn't brought about until 2009. The issues are unrelated.
So, these should show that the arguments people have against common core are wrong. At best, they're uninformed; at worst, they're intentionally lying.