The short answer is there are a variety of reasons. This actually goes into law a little bit so I will be in uncharted territory.

So Davis was indicted for treason. But when he went before the judge his team argued that due to the 14th Amendment he was already punished for insurrection against the US, as under the 14th Amendment anyone who takes an oath of public office and commits an insurrection can no longer hold public office.

However the chief justice gave him an interesting argument. As Davis was president of another nation, he wasn't technically a citizen and couldn't be tried for treason for that reason.

In the end, Andrew Johnson pardoned him and all ex-confederates anyways, so any outcome would have been moot due to this.