I thought I might share my personal experience as a child from a large family. I know this does not o for all large families, but I have met people with similar experiences.
I grew up as the oldest of six children. My parents started homeschooling us because of terrible the terrible school system in Las Vegas, Nevada, but continued to home school because of religious reasons. Both my stepmother and my father were ill-equipped to be teachers, my stepmother would just hand us books and expect us to learn from those and could never answer any questions we asked. Gradually we were doing less and less school work and education became training to be "good wives and mothers". My father, instead of focusing on schoolwork, was more concerned that the house was kept perfectly clean and that the day was spent doing errands. Sometimes the errand was running to the mall to pick up a new video game he wanted.
When we moved to Alaska I was happy, because they offered Home School groups that monitored school work (to make sure school was actually being done) and offered financial assistance to families. It was the first time since we started that I actually had a curriculum. That didn't last long however as half the time we didn't follow the curriculum and my stepmother decided to no longer use the group, because she didn't like it telling her what to do. (Also financial assistance did not cover Religious curriculum)
She convinced me to get my GED at 16 so I could go to college sooner. (I now regret listening to her as it can actually be harder to get into some universities). Not only that my parents wouldn't even let me go to college if it meant moving away from them. (I am now safely away from them in Texas, they are in South Dakota, it was a bold move and the result was them accusing my real mother of leading us astray under the influence of Satan.)
I now struggle everyday with my lack of education (I have a GED but my education is equivalent to that of a fifth grader, the last grade I was in public in school) I also have very poor social skills.
I know this is my individual experience, but since religion and home school are common themes in large families, I expect there are many more like me.
And with an experience like mine I can see why kids in large families do not fare very well academically.