Context #1

Andrew: Last week’s assignment was due two days ago. Why haven’t you finished it yet?
Mia: Andrew, you know I’ve been having some personal problems. Please
cut me some slack.
Andrew:There are no exceptions. If I cut
you some slack, then everyone will want me to cut some slackfor them. 
Mia:You’re so inflexible. I wish you would be more understanding.
Andrew:I would cut
you some slack if you didn’t have a habit of turning assignments in late.

Context #2

Jeff: I’ve reported a student for using his phone during class time.
Michelle: Why can’t you cut
the student some slack? Maybe the
student had a legitimate emergency.
Jeff:He was checking facebook. How would the student benefit from me cutting him some slack?
Michelle:I guess there’s no excuse. You never cut anyone some slack sometimes though?
Jeff:Students get more than enough warnings before
being reported. This student doesn’t
deserve any slack. He does this daily.

Meaning:The expression
“cut somebody some slack”
means to give someone permission to do something not normally allowed or to be
less strict about something (e.g. a policy or rule). In this example, Mia was upset that Andrew
didn’t allow for additional time to finish her assignment. However, Andrew is unwilling to be more
flexible because Mia has had a habit of turning things in late. So he is less willing to cut Mia some slack. In the
second example, the teacher was upset that the student was focusing on his
phone everyday and had been warned about the rules previously. The teacher didn’t think giving the student
any more chances (cutting any slack) was of benefit to him or the student.

https://languagesystems.edu/