U.S. school systems are organized by grades. There's no general rule because education in the U.S. is decentralized, but often students will enter first grade at age 6, second grade at age 7, third grade at age 8, and so on. Often, "promotion" to the next grade is almost automatic. Let's say a student is in fifth grade. Normally, next year, at age eleven, he would enter sixth grade.
But, depending on the school system and the educational theories of the day, if a student does poorly in fifth grade, they may decide that it is better for him to be "held back." He stays in fifth grade, an eleven-year-old in a class of mostly ten-year-olds, and gets a second chance to repeat the work.
Naturally, children are cruel and regard "being held back" as a sign of stupidity. Apparently the girl has actually been held back. The brother is saying "if you think Dad is going to put up with this diet, you are stupid--so stupid that behind held back one year wasn't enough, you should have been held back for another year."