Lyric discussion by yeslewis 

Cover art for Sheets lyrics by Damien Jurado

It's not "I'll share the trap that you have me in". It's "I won't share the trap you have me in". Listen closely, and think about the meaning!

Lyric Correction

Agreed! She's like a fisherman that's caught these two fish (the guys) in a trap, and he's telling her to send the one back to the water so he doesn't have to share the trap with this other guy.