And the four associate justice who agreed with him? What was their excuse?
Chase told Stanton, 'If you bring these leaders to trial [Davis & Benjamin], it will condemn the North, for by the Constitution, secession is not rebellion', and that Davis capture was a mistake, and his 'trial will be a greater one. We cannot convict him of treason.'
But that's not what Chase said. His position was that trying and convicting Davis and the other leaders of the rebellion would be a violation of their 5th Amendment protections. Since the 14th Amendment prevented the leaders of the office from holding office again, Chief Justice Chase believed that trial and conviction for treason would mean that they would be punished again for the same crime. You are right that Davis wanted a trial, but when the Chief Justice made his position clear Davis's lawyers pushed for a dismissal. They knew, even if Davis did not, that a trial would mean conviction. No other outcome would have been possible.
Davis was arrested in 1865. The government could had held a trial and convicted Davis, and then executed him if found guilty. Instead, they understood that to bring him to trial would validate secession (see Chase's statement above). The 14th (ratified three years later) contained a clause allowing Congress to remove the prohibition against holding office - no dual punishmemt necessary. Cahse just made it up.
After Jeff Davis was captured, the vindictive radical Yankee Secretary of War Edwin Stanton [who some feel may have known more about Lincoln's assassination than is admitted] wanted to implicate Davis both as a co-conspirator in Lincoln's assassination and as a traitor for leading the secessionist government in Richmond, even though secession had not been original with Davis. Try as they might, the radical Republicans in Washington couldn't quite bring it off. Burke Davis notes, on page 204 of his book, a quote by Chief Justice Salmom P. Chase, telling Stanton "If you bring these leaders to trial, it will condemn the North, for by the Constitution, secession is not rebellion....His [Jeff Davis'] capture was a mistake. His trial will be a greater one. We cannot convict him of treason. Secession is settled. Let it stay settled." Burke Davis continued on page 214 of the book, noting that a congressional committee proposed a special court for Davis' trial, headed by Judge Franz Lieber. Davis noted: "After studying more than 270,000 Confederate documents, seeking evidence against Davis, this court discouraged the War Department: 'Davis will be found not guilty,' Lieber reported, 'and we shall stand there completely beaten'." What the radical Northern politicians were admitting among themselves [but not for the historical record] was that they had just fought a 'civil war' that had taken or maimed the lives of over 600,000 Americans, both North and South, and they had no constitutional justification for having done so, nor had they had any constitutional right to impede the Southern states when they chose to withdraw from the constitutional compact. They had fought solely for the right to keep an empire together. Call it 'manifest destiny' or whatever other noble-sounding euphemism you may tack onto it, either way, they had been wrong. Now they could not afford to let Jeff Davis go to trial, else their grievous crime would become public knowledge and beget them even more problems in the future. Needless to say, you probably have not read much about this in most of your 'history' books. As the narrator at the beginning of the movie Braveheart so correctly stated: "History is written by those who've hanged heroes."