Machine
You have a private mouth that's a machine. But you have to keep your machine mouth private because it would scare all the non-machine people around you.
Doesn't this kanji look like a machine mouth? Now wouldn't you want to keep that private from the people you know?
だい, たい
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To make sure they can't tell what's machine and what's human, you dye (だい) the mouth to make it look like skin. You find dye the same shade as your normal mouth and just slap it on there.
Imagine being so afraid that people will find out about your machine mouth that you have to dye it to match a normal human mouth. Oh, when will this discrimination against machine-kind end?!