I see no sense, and this crying and grieving will
both double our laundry if you live without me.

The story:

The song made sense to me up until that part. She
was trying to tell the boy she didn't want a serious
relationship. Got it. But then she said the laundry
(literal or figurative) would double if he lives
without her? Wait.. What? I tried to make sense of
it for years. Then I just went and looked it up. The
real lyrics make way more sense but I still hear
mine when I listen to the song.