This happened to not only my son but me as well. I will give you my personal opinion.
I still remember my friends going to first grade and I had to remain in the same class with the same teacher. I didn't understand why I wasn't able to advance. Although I was incredibly intelligent, my social skills were lacking. The kindergarten teacher pressured my mother to hold me back. She did and she regretted it. My birthday was Oct 2. So I entered kindergarten 4 turning 5.
I can tell you that in Jr. High and High school that year was a huge difference. I rarely hung out with people in my grade and was quite annoyed with my class members. I loved high school but that year of difference of me being 18 almost 19, not 17 almost 18 was quite evident.
My son turned 5 on October 30th. While he is quite smart, I do not feel that he is mature-social enough or advanced enough to go to kindergarten. He is also a smaller boy. There were many reasons to keep him in his t-k class. I do see other children, much more advanced than my child, who socialize well, follow directions and overall should be in kinder.
To my knowledge, this is a situation that cannot be fought. I understand being bored all day. I went through many days like that in high school. It just will prepare them for life. Don't rush them through school but also do not hold them back!