off

Today a student said to me
I have two days free next week meaning two days off.
free in Spanish means libre, like not in captivity; it also means  free of charge, without paying.
We use tener un día libre, meaning not to work. so here is the misunderstanding.
Once told that the equivalent expression is take a day off, take a week off, or maybe be off two days, she struggled to understand the idea of off as in not working!
Welcome to English
off is not used just as turn on / turn off
food is off
you are off food
you are off = leave
you are off = you are not working (on a specific day)
time off= free time
take time off= stop working (doing sth for a while)
sth came off = desprenderse
the bomb/ alarm went off = sonó se disparó.
go off to ..= leave for..
head off = leave
etc.
subject person or thing? 
what verb does it go with?
context?
Crazy English!