Based on the evidence in Just Mercy, why are wrongful convictions and illegal trials involving young children very common?

Young children are considered very unreliable witnesses. Their memories are not fully developed and they are more vulnerable to the emotional pressures associated with interrogation. The memories they do have are easily manipulated by prosecutors' lines of questioning, particularly questions that are suggestive and lean toward certain answers. These observations are supported by contemporary psychologists and lawyers. This is just to give you perspective on children as witnesses (this will become relevant in a few paragraphs).
Just Mercy: A Story of Justice and Redemption explores the opposite perspective in which juveniles are wrongfully persecuted. Bryan Stevenson offers an authoritative perspective as a lawyer. In the 1980s and 1990s, he represented juveniles in Alabama, the state which had the most children sentenced to death per capita in the country. During this time, children could be sentenced to die in the United States.
Stevenson notes a vast number of issues in the justice system associated with juveniles. He asserts that children should never be tried in an adult court; even a child of 14 cannot adequately defend themselves in the adult criminal justice system. Issues also arise when another child (or multiple children) testify against another child, as I mentioned previously. These same issues can be seen with children who have been convicted; in particular, there is a common phenomenon referred to as "confession contamination," which is a tactic that can be used to illicit false confessions and operates on the same principles as a witness testimony.
Moreover, there are a substantial number of cases in which juveniles are tried for murder using a firearm. For example, if a child is being physically abused by a parent or guardian, they are unable to effectively defend themselves using physical force. There are also many cases in which children have been convicted of murder using a firearm to defend a sibling or a parent from another adult.
Issues also arise in cases involving rape and self-defence cases. In rape trials, DNA evidence is required. Many children are uncomfortable disclosing the fact that they have been raped, and some never feel comfortable disclosing this—especially if it involves a parent, sibling, or family friend.