Don't Want to Miss a Thing

I just finished watching Armageddon and it reminds me of an issue I have with the grammar of the Aerosmith/Dianne Warren song “Don’t Want to Miss a Thing.” The lyrics go “…don’t want to fall asleep / ‘cause I miss you babe / and I don’t want to miss a thing.”

I can’t help but hear this the wrong way – it’s my contrary nature. My interpretation is that he’s singing “I miss you. You’re an object. I don’t want to miss an object, so I don’t want to miss you.” It’s analogous to saying “‘cause I miss you babe / and I don’t want to miss a blockhead.”

Anyway, I know he isn’t saying anything of the kind, but the proximity of two uses of “thing” makes this an automatic alternative my brain entertains.