President Jefferson Davis demanded a treason trial after he was incarcerated. It was decide that to put him on trial would put the issue of secession on trial. The USA thought they would lose the case and that would be to embarrassing. Davis was eventually let free.
Exactly.
If you bring these [Confederate] leaders to trial it will condemn the North, for by the Constitution secession is not rebellion. Lincoln wanted Davis to escape, and he was right. His capture was a mistake. His trial will be a greater one. Chief Justice Salmon P. Chase, July 1867 (Foote, The Civil War, Vol. 3, p. 765)
If you bring these leaders to trial, it will condemn the North, for by the Constitution, secession is not a rebellion. His [Jefferson Davis] capture was a mistake. His trial will be a greater one. We cannot convict him of treason. [as quoted by Herman S. Frey, in Jefferson Davis, Frey Enterprises, 1977, pp. 69-72]