I am having a hard time understanding why, help me out. I’m not sure about airports, but the US doesn’t check passports on the way out at land borders, so you could walk from the US into Mexico without the US side checking, and then when the Mexican official asks you, you could just present your German passport. Of course American citizens are obliged to reenter the US on their American passport, but if you are getting the new US passport back by post, couldn’t you have a family member DHL it to wherever you are outside the US?