Your assertion about why parents dislike this math is wrong on at least a couple of levels.
When my children were taught common-core math (5th grade) the teachers began the year explaining to parents “we don’t care as much that your children get the right answer, we’re more interested in their logic to get the answer they came to.” This is fundamentally wrong. If nothing else in life is right or wrong — math is. There is a right answer to 2+2 and it will always be 4.
My second reason for disliking common core math is the problem of speed. My children are in a private school now and they are fundamentally disadvantaged against children taught traditional math. The reason? Speed. It takes them more than double the amount of time to come to the same answer as traditional math students. In a world of timed tests and a tremendous emphasis on speed now in education, they are struggling to overcome the deficit left by their common-core teachers.