One of the things to remember is the nazi crimes against humanity trials were essentially unprecedented. There wasn't much of an international court system at the time. The trials happened mostly because so many people were horrified by what had been done (more or less) legally. The nazis really believed in their own righteousness and the technically legal status of the actions they had taken. A repeated response to 'how dare you commit these crimes?' was 'They were not crimes in Germany,' or 'The government was illegitimate, and therefore crimes committed against it were legitimate,' or 'Those were crimes of self-defense because [we believed] the victims were seeking our destruction,' or 'Our courts ruled that was legal,' etc.
They were racist loons, but to understand their position, imagine a group of your neighbors, who you know have gotten up to some hinky shit of their own in their own homes, grouped together, kicked the shit out of you, and then locked you in your bathroom until they could set up a courtroom in your home, and proceed to harangue you about how you treated your step-son. If that happened, it's very unlikely you'd accept the legal or moral authority of your captors. You know you won't get away, and you know you're dead anyway if you stonewall, (you also have no 5th ammendment to plead.) so you may as well say your bit and try to sway someone to your side. Heck, your neighbor America has always had some very similarly grim views regarding the treatment of step-sons. Maybe you can get him to help you.
The oft repeated 'don't say anything' response to being arrested is only applicable in places where you think you can trust the court and you think there's a chance they might not be able to prove you are guilty. If you know they have all the proof, you might as well try to nullify the jury since that's your only hope.