What? An airplane is 飞机，where 飞 = flying and 机 = machine

I think the confusion is because of simplified vs. traditional characters. 机 is made from 木 (wood) and 几 (table) radicals, and in Japanese it really does mean desk/table. But in Chinese it's the simplified form of 機 (machine). The 几 is just a substitute for some more complicated strokes, and 木 is just for the sound.

Even then the character by itself doesn't mean "airplane", you need to pair it with 飞.